{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0001","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":1,\"ratio\":[1,7],\"shift\":1,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/7, 1, 否, a_n=1*(1/7)^n/(n+1), abs_ratio=1/7*(n+1)/(n+2), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(1, 1/7, 1, 否, a_n=1*(1/7)^n/(n+1), abs_ratio=1/7*(n+1)/(n+2), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172001,"parameters":{"scale":1,"ratio":[1,7],"shift":1,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,7],scale:[1,1],shift:1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0002","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":2,\"ratio\":[2,8],\"shift\":2,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/4, 2, 是, a_n=2*(-1)^n*(1/4)^n/(n+2), abs_ratio=1/4*(n+2)/(n+3), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(2, 1/4, 2, 是, a_n=2*(-1)^n*(1/4)^n/(n+2), abs_ratio=1/4*(n+2)/(n+3), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172002,"parameters":{"scale":2,"ratio":[2,8],"shift":2,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,4],scale:[2,1],shift:2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0003","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":3,\"ratio\":[3,9],\"shift\":3,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/3, 3, 否, a_n=3*(1/3)^n/(n+3), abs_ratio=1/3*(n+3)/(n+4), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(3, 1/3, 3, 否, a_n=3*(1/3)^n/(n+3), abs_ratio=1/3*(n+3)/(n+4), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172003,"parameters":{"scale":3,"ratio":[3,9],"shift":3,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,3],scale:[3,1],shift:3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0004","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":4,\"ratio\":[4,10],\"shift\":4,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 2/5, 4, 是, a_n=4*(-1)^n*(2/5)^n/(n+4), abs_ratio=2/5*(n+4)/(n+5), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(4, 2/5, 4, 是, a_n=4*(-1)^n*(2/5)^n/(n+4), abs_ratio=2/5*(n+4)/(n+5), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172004,"parameters":{"scale":4,"ratio":[4,10],"shift":4,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[2,5],scale:[4,1],shift:4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0005","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":5,\"ratio\":[5,11],\"shift\":5,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 5/11, 5, 否, a_n=5*(5/11)^n/(n+5), abs_ratio=5/11*(n+5)/(n+6), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(5, 5/11, 5, 否, a_n=5*(5/11)^n/(n+5), abs_ratio=5/11*(n+5)/(n+6), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172005,"parameters":{"scale":5,"ratio":[5,11],"shift":5,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[5,11],scale:[5,1],shift:5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0006","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":6,\"ratio\":[1,7],\"shift\":6,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 1/7, 6, 是, a_n=6*(-1)^n*(1/7)^n/(n+6), abs_ratio=1/7*(n+6)/(n+7), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(6, 1/7, 6, 是, a_n=6*(-1)^n*(1/7)^n/(n+6), abs_ratio=1/7*(n+6)/(n+7), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172006,"parameters":{"scale":6,"ratio":[1,7],"shift":6,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,7],scale:[6,1],shift:6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0007","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":7,\"ratio\":[2,8],\"shift\":7,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 1/4, 7, 否, a_n=7*(1/4)^n/(n+7), abs_ratio=1/4*(n+7)/(n+8), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(7, 1/4, 7, 否, a_n=7*(1/4)^n/(n+7), abs_ratio=1/4*(n+7)/(n+8), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172007,"parameters":{"scale":7,"ratio":[2,8],"shift":7,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,4],scale:[7,1],shift:7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0008","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":8,\"ratio\":[3,9],\"shift\":8,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 1/3, 8, 是, a_n=8*(-1)^n*(1/3)^n/(n+8), abs_ratio=1/3*(n+8)/(n+9), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(8, 1/3, 8, 是, a_n=8*(-1)^n*(1/3)^n/(n+8), abs_ratio=1/3*(n+8)/(n+9), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172008,"parameters":{"scale":8,"ratio":[3,9],"shift":8,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,3],scale:[8,1],shift:8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0009","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":9,\"ratio\":[4,10],\"shift\":9,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 2/5, 9, 否, a_n=9*(2/5)^n/(n+9), abs_ratio=2/5*(n+9)/(n+10), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(9, 2/5, 9, 否, a_n=9*(2/5)^n/(n+9), abs_ratio=2/5*(n+9)/(n+10), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172009,"parameters":{"scale":9,"ratio":[4,10],"shift":9,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[2,5],scale:[9,1],shift:9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0010","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":10,\"ratio\":[5,11],\"shift\":10,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 5/11, 10, 是, a_n=10*(-1)^n*(5/11)^n/(n+10), abs_ratio=5/11*(n+10)/(n+11), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(10, 5/11, 10, 是, a_n=10*(-1)^n*(5/11)^n/(n+10), abs_ratio=5/11*(n+10)/(n+11), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172010,"parameters":{"scale":10,"ratio":[5,11],"shift":10,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[5,11],scale:[10,1],shift:10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0011","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":11,\"ratio\":[1,7],\"shift\":11,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 1/7, 11, 否, a_n=11*(1/7)^n/(n+11), abs_ratio=1/7*(n+11)/(n+12), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(11, 1/7, 11, 否, a_n=11*(1/7)^n/(n+11), abs_ratio=1/7*(n+11)/(n+12), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172011,"parameters":{"scale":11,"ratio":[1,7],"shift":11,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,7],scale:[11,1],shift:11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0012","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":12,\"ratio\":[2,8],\"shift\":12,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 1/4, 12, 是, a_n=12*(-1)^n*(1/4)^n/(n+12), abs_ratio=1/4*(n+12)/(n+13), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(12, 1/4, 12, 是, a_n=12*(-1)^n*(1/4)^n/(n+12), abs_ratio=1/4*(n+12)/(n+13), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172012,"parameters":{"scale":12,"ratio":[2,8],"shift":12,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,4],scale:[12,1],shift:12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0013","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":13,\"ratio\":[3,9],\"shift\":13,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 1/3, 13, 否, a_n=13*(1/3)^n/(n+13), abs_ratio=1/3*(n+13)/(n+14), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(13, 1/3, 13, 否, a_n=13*(1/3)^n/(n+13), abs_ratio=1/3*(n+13)/(n+14), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172013,"parameters":{"scale":13,"ratio":[3,9],"shift":13,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,3],scale:[13,1],shift:13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0014","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":14,\"ratio\":[4,10],\"shift\":14,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 2/5, 14, 是, a_n=14*(-1)^n*(2/5)^n/(n+14), abs_ratio=2/5*(n+14)/(n+15), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(14, 2/5, 14, 是, a_n=14*(-1)^n*(2/5)^n/(n+14), abs_ratio=2/5*(n+14)/(n+15), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172014,"parameters":{"scale":14,"ratio":[4,10],"shift":14,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[2,5],scale:[14,1],shift:14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0015","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":15,\"ratio\":[5,11],\"shift\":15,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 5/11, 15, 否, a_n=15*(5/11)^n/(n+15), abs_ratio=5/11*(n+15)/(n+16), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(15, 5/11, 15, 否, a_n=15*(5/11)^n/(n+15), abs_ratio=5/11*(n+15)/(n+16), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172015,"parameters":{"scale":15,"ratio":[5,11],"shift":15,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[5,11],scale:[15,1],shift:15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0016","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":16,\"ratio\":[1,7],\"shift\":16,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 1/7, 16, 是, a_n=16*(-1)^n*(1/7)^n/(n+16), abs_ratio=1/7*(n+16)/(n+17), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(16, 1/7, 16, 是, a_n=16*(-1)^n*(1/7)^n/(n+16), abs_ratio=1/7*(n+16)/(n+17), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172016,"parameters":{"scale":16,"ratio":[1,7],"shift":16,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,7],scale:[16,1],shift:16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0017","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":17,\"ratio\":[2,8],\"shift\":17,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 1/4, 17, 否, a_n=17*(1/4)^n/(n+17), abs_ratio=1/4*(n+17)/(n+18), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(17, 1/4, 17, 否, a_n=17*(1/4)^n/(n+17), abs_ratio=1/4*(n+17)/(n+18), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172017,"parameters":{"scale":17,"ratio":[2,8],"shift":17,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,4],scale:[17,1],shift:17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0018","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":18,\"ratio\":[3,9],\"shift\":18,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 1/3, 18, 是, a_n=18*(-1)^n*(1/3)^n/(n+18), abs_ratio=1/3*(n+18)/(n+19), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(18, 1/3, 18, 是, a_n=18*(-1)^n*(1/3)^n/(n+18), abs_ratio=1/3*(n+18)/(n+19), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172018,"parameters":{"scale":18,"ratio":[3,9],"shift":18,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,3],scale:[18,1],shift:18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0019","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":19,\"ratio\":[4,10],\"shift\":19,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 2/5, 19, 否, a_n=19*(2/5)^n/(n+19), abs_ratio=2/5*(n+19)/(n+20), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(19, 2/5, 19, 否, a_n=19*(2/5)^n/(n+19), abs_ratio=2/5*(n+19)/(n+20), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172019,"parameters":{"scale":19,"ratio":[4,10],"shift":19,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[2,5],scale:[19,1],shift:19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0020","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":20,\"ratio\":[5,11],\"shift\":20,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 5/11, 20, 是, a_n=20*(-1)^n*(5/11)^n/(n+20), abs_ratio=5/11*(n+20)/(n+21), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(20, 5/11, 20, 是, a_n=20*(-1)^n*(5/11)^n/(n+20), abs_ratio=5/11*(n+20)/(n+21), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172020,"parameters":{"scale":20,"ratio":[5,11],"shift":20,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[5,11],scale:[20,1],shift:20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0021","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":21,\"ratio\":[1,7],\"shift\":21,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 1/7, 21, 否, a_n=21*(1/7)^n/(n+21), abs_ratio=1/7*(n+21)/(n+22), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(21, 1/7, 21, 否, a_n=21*(1/7)^n/(n+21), abs_ratio=1/7*(n+21)/(n+22), limit=1/7, 4/7, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172021,"parameters":{"scale":21,"ratio":[1,7],"shift":21,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,7],scale:[21,1],shift:21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0022","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":22,\"ratio\":[2,8],\"shift\":22,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 1/4, 22, 是, a_n=22*(-1)^n*(1/4)^n/(n+22), abs_ratio=1/4*(n+22)/(n+23), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(22, 1/4, 22, 是, a_n=22*(-1)^n*(1/4)^n/(n+22), abs_ratio=1/4*(n+22)/(n+23), limit=1/4, 5/8, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172022,"parameters":{"scale":22,"ratio":[2,8],"shift":22,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[1,4],scale:[22,1],shift:22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0023","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":23,\"ratio\":[3,9],\"shift\":23,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 1/3, 23, 否, a_n=23*(1/3)^n/(n+23), abs_ratio=1/3*(n+23)/(n+24), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(23, 1/3, 23, 否, a_n=23*(1/3)^n/(n+23), abs_ratio=1/3*(n+23)/(n+24), limit=1/3, 2/3, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172023,"parameters":{"scale":23,"ratio":[3,9],"shift":23,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[1,3],scale:[23,1],shift:23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0024","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":24,\"ratio\":[4,10],\"shift\":24,\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 2/5, 24, 是, a_n=24*(-1)^n*(2/5)^n/(n+24), abs_ratio=2/5*(n+24)/(n+25), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(24, 2/5, 24, 是, a_n=24*(-1)^n*(2/5)^n/(n+24), abs_ratio=2/5*(n+24)/(n+25), limit=2/5, 7/10, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172024,"parameters":{"scale":24,"ratio":[4,10],"shift":24,"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:true,ratio:[2,5],scale:[24,1],shift:24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0025","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-nonconstant-convergent；資料={\"scale\":25,\"ratio\":[5,11],\"shift\":25,\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 5/11, 25, 否, a_n=25*(5/11)^n/(n+25), abs_ratio=5/11*(n+25)/(n+26), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)","explanation_zh":"Wave6第十一層核對=(25, 5/11, 25, 否, a_n=25*(5/11)^n/(n+25), abs_ratio=5/11*(n+25)/(n+26), limit=5/11, 8/11, 是, eventual_geometric_domination, absolutely_convergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-nonconstant-convergent","seed":202611172025,"parameters":{"scale":25,"ratio":[5,11],"shift":25,"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-nonconstant-convergent","semantic_template":"ratio-nonconstant-convergent|{alternating:false,ratio:[5,11],scale:[25,1],shift:25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0026","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":1,\"ratio\":[6,3],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 否, 2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(1, 2, 否, 2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172026,"parameters":{"scale":1,"ratio":[6,3],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[2,1],scale:[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0027","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":2,\"ratio\":[7,4],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 7/4, 是, 7/4, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(2, 7/4, 是, 7/4, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172027,"parameters":{"scale":2,"ratio":[7,4],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[7,4],scale:[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0028","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":3,\"ratio\":[8,5],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 8/5, 否, 8/5, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(3, 8/5, 否, 8/5, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172028,"parameters":{"scale":3,"ratio":[8,5],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[8,5],scale:[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0029","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":4,\"ratio\":[9,6],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 3/2, 是, 3/2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(4, 3/2, 是, 3/2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172029,"parameters":{"scale":4,"ratio":[9,6],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[3,2],scale:[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0030","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":5,\"ratio\":[10,7],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 10/7, 否, 10/7, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(5, 10/7, 否, 10/7, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172030,"parameters":{"scale":5,"ratio":[10,7],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[10,7],scale:[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0031","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":6,\"ratio\":[6,3],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 2, 是, 2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(6, 2, 是, 2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172031,"parameters":{"scale":6,"ratio":[6,3],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[2,1],scale:[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0032","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":7,\"ratio\":[7,4],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 7/4, 否, 7/4, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(7, 7/4, 否, 7/4, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172032,"parameters":{"scale":7,"ratio":[7,4],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[7,4],scale:[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0033","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":8,\"ratio\":[8,5],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 8/5, 是, 8/5, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(8, 8/5, 是, 8/5, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172033,"parameters":{"scale":8,"ratio":[8,5],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[8,5],scale:[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0034","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":9,\"ratio\":[9,6],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 3/2, 否, 3/2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(9, 3/2, 否, 3/2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172034,"parameters":{"scale":9,"ratio":[9,6],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[3,2],scale:[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0035","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":10,\"ratio\":[10,7],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 10/7, 是, 10/7, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(10, 10/7, 是, 10/7, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172035,"parameters":{"scale":10,"ratio":[10,7],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[10,7],scale:[10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0036","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":11,\"ratio\":[6,3],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 2, 否, 2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(11, 2, 否, 2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172036,"parameters":{"scale":11,"ratio":[6,3],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[2,1],scale:[11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0037","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":12,\"ratio\":[7,4],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 7/4, 是, 7/4, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(12, 7/4, 是, 7/4, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172037,"parameters":{"scale":12,"ratio":[7,4],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[7,4],scale:[12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0038","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":13,\"ratio\":[8,5],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 8/5, 否, 8/5, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(13, 8/5, 否, 8/5, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172038,"parameters":{"scale":13,"ratio":[8,5],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[8,5],scale:[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0039","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":14,\"ratio\":[9,6],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 3/2, 是, 3/2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(14, 3/2, 是, 3/2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172039,"parameters":{"scale":14,"ratio":[9,6],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[3,2],scale:[14,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0040","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":15,\"ratio\":[10,7],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 10/7, 否, 10/7, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(15, 10/7, 否, 10/7, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172040,"parameters":{"scale":15,"ratio":[10,7],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[10,7],scale:[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0041","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":16,\"ratio\":[6,3],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 2, 是, 2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(16, 2, 是, 2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172041,"parameters":{"scale":16,"ratio":[6,3],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[2,1],scale:[16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0042","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":17,\"ratio\":[7,4],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 7/4, 否, 7/4, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(17, 7/4, 否, 7/4, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172042,"parameters":{"scale":17,"ratio":[7,4],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[7,4],scale:[17,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0043","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":18,\"ratio\":[8,5],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 8/5, 是, 8/5, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(18, 8/5, 是, 8/5, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172043,"parameters":{"scale":18,"ratio":[8,5],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[8,5],scale:[18,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0044","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":19,\"ratio\":[9,6],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 3/2, 否, 3/2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(19, 3/2, 否, 3/2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172044,"parameters":{"scale":19,"ratio":[9,6],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[3,2],scale:[19,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0045","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":20,\"ratio\":[10,7],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 10/7, 是, 10/7, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(20, 10/7, 是, 10/7, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172045,"parameters":{"scale":20,"ratio":[10,7],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[10,7],scale:[20,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0046","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":21,\"ratio\":[6,3],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 2, 否, 2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(21, 2, 否, 2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172046,"parameters":{"scale":21,"ratio":[6,3],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[2,1],scale:[21,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0047","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":22,\"ratio\":[7,4],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 7/4, 是, 7/4, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(22, 7/4, 是, 7/4, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172047,"parameters":{"scale":22,"ratio":[7,4],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[7,4],scale:[22,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0048","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":23,\"ratio\":[8,5],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 8/5, 否, 8/5, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(23, 8/5, 否, 8/5, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172048,"parameters":{"scale":23,"ratio":[8,5],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[8,5],scale:[23,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0049","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":24,\"ratio\":[9,6],\"alternating\":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 3/2, 是, 3/2, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(24, 3/2, 是, 3/2, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172049,"parameters":{"scale":24,"ratio":[9,6],"alternating":true,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:true,ratio:[3,2],scale:[24,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0050","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-geometric-divergent；資料={\"scale\":25,\"ratio\":[10,7],\"alternating\":false}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 10/7, 否, 10/7, terms_do_not_tend_to_zero, divergent)","explanation_zh":"Wave6第十一層核對=(25, 10/7, 否, 10/7, terms_do_not_tend_to_zero, divergent)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-geometric-divergent","seed":202611172050,"parameters":{"scale":25,"ratio":[10,7],"alternating":false,"domain":"Exact_ratio_test_series","operation":"ratio-geometric-divergent","semantic_template":"ratio-geometric-divergent|{alternating:false,ratio:[10,7],scale:[25,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0051","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1, abs_ratio=((n+1)/(n+2))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 1, abs_ratio=((n+1)/(n+2))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172051,"parameters":{"exponent":1,"shift":1,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0052","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, abs_ratio=((n+2)/(n+3))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 2, abs_ratio=((n+2)/(n+3))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172052,"parameters":{"exponent":2,"shift":2,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0053","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 3, abs_ratio=((n+3)/(n+4))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 3, abs_ratio=((n+3)/(n+4))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172053,"parameters":{"exponent":1,"shift":3,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0054","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 4, abs_ratio=((n+4)/(n+5))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 4, abs_ratio=((n+4)/(n+5))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172054,"parameters":{"exponent":2,"shift":4,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0055","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 5, abs_ratio=((n+5)/(n+6))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 5, abs_ratio=((n+5)/(n+6))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172055,"parameters":{"exponent":1,"shift":5,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0056","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 6, abs_ratio=((n+6)/(n+7))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 6, abs_ratio=((n+6)/(n+7))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172056,"parameters":{"exponent":2,"shift":6,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0057","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 7, abs_ratio=((n+7)/(n+8))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 7, abs_ratio=((n+7)/(n+8))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172057,"parameters":{"exponent":1,"shift":7,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0058","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 8, abs_ratio=((n+8)/(n+9))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 8, abs_ratio=((n+8)/(n+9))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172058,"parameters":{"exponent":2,"shift":8,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0059","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 9, abs_ratio=((n+9)/(n+10))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 9, abs_ratio=((n+9)/(n+10))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172059,"parameters":{"exponent":1,"shift":9,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0060","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 10, abs_ratio=((n+10)/(n+11))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 10, abs_ratio=((n+10)/(n+11))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172060,"parameters":{"exponent":2,"shift":10,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0061","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 11, abs_ratio=((n+11)/(n+12))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 11, abs_ratio=((n+11)/(n+12))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172061,"parameters":{"exponent":1,"shift":11,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0062","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 12, abs_ratio=((n+12)/(n+13))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 12, abs_ratio=((n+12)/(n+13))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172062,"parameters":{"exponent":2,"shift":12,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0063","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 13, abs_ratio=((n+13)/(n+14))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 13, abs_ratio=((n+13)/(n+14))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172063,"parameters":{"exponent":1,"shift":13,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0064","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 14, abs_ratio=((n+14)/(n+15))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 14, abs_ratio=((n+14)/(n+15))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172064,"parameters":{"exponent":2,"shift":14,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0065","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 15, abs_ratio=((n+15)/(n+16))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 15, abs_ratio=((n+15)/(n+16))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172065,"parameters":{"exponent":1,"shift":15,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0066","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 16, abs_ratio=((n+16)/(n+17))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 16, abs_ratio=((n+16)/(n+17))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172066,"parameters":{"exponent":2,"shift":16,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0067","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 17, abs_ratio=((n+17)/(n+18))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 17, abs_ratio=((n+17)/(n+18))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172067,"parameters":{"exponent":1,"shift":17,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0068","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 18, abs_ratio=((n+18)/(n+19))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 18, abs_ratio=((n+18)/(n+19))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172068,"parameters":{"exponent":2,"shift":18,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0069","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 19, abs_ratio=((n+19)/(n+20))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 19, abs_ratio=((n+19)/(n+20))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172069,"parameters":{"exponent":1,"shift":19,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0070","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 20, abs_ratio=((n+20)/(n+21))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 20, abs_ratio=((n+20)/(n+21))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172070,"parameters":{"exponent":2,"shift":20,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0071","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 21, abs_ratio=((n+21)/(n+22))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 21, abs_ratio=((n+21)/(n+22))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172071,"parameters":{"exponent":1,"shift":21,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0072","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 22, abs_ratio=((n+22)/(n+23))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 22, abs_ratio=((n+22)/(n+23))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172072,"parameters":{"exponent":2,"shift":22,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0073","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 23, abs_ratio=((n+23)/(n+24))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 23, abs_ratio=((n+23)/(n+24))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172073,"parameters":{"exponent":1,"shift":23,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0074","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":2,\"shift\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 24, abs_ratio=((n+24)/(n+25))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(2, 24, abs_ratio=((n+24)/(n+25))^2, 1, convergent_p_series, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172074,"parameters":{"exponent":2,"shift":24,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:2,shift:24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0075","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-limit-one-inconclusive；資料={\"exponent\":1,\"shift\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 25, abs_ratio=((n+25)/(n+26))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)","explanation_zh":"Wave6第十一層核對=(1, 25, abs_ratio=((n+25)/(n+26))^1, 1, divergent_harmonic_tail, L_equal_one_is_inconclusive)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-limit-one-inconclusive","seed":202611172075,"parameters":{"exponent":1,"shift":25,"domain":"Exact_ratio_test_series","operation":"ratio-limit-one-inconclusive","semantic_template":"ratio-limit-one-inconclusive|{exponent:1,shift:25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0076","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 2, a_n=2_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 2, a_n=2_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172076,"parameters":{"mode":"zero_terms","scale":2,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0077","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"finite_samples\",\"scale\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_samples, 3, ratios_equal_1/2_for_n<=3_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)","explanation_zh":"Wave6第十一層核對=(finite_samples, 3, ratios_equal_1/2_for_n<=3_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172077,"parameters":{"mode":"finite_samples","scale":3,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"finite_samples\",scale:3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0078","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"missing_limit\",\"scale\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(missing_limit, 4, absolute_ratios_alternate_between_1/5_and_5, limit_does_not_exist, 否)","explanation_zh":"Wave6第十一層核對=(missing_limit, 4, absolute_ratios_alternate_between_1/5_and_5, limit_does_not_exist, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172078,"parameters":{"mode":"missing_limit","scale":4,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"missing_limit\",scale:4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0079","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"signed_without_absolute\",\"scale\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_without_absolute, 5, a_n=(-1)^n*5*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)","explanation_zh":"Wave6第十一層核對=(signed_without_absolute, 5, a_n=(-1)^n*5*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172079,"parameters":{"mode":"signed_without_absolute","scale":5,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"signed_without_absolute\",scale:5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0080","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 6, a_n=6_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 6, a_n=6_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172080,"parameters":{"mode":"zero_terms","scale":6,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0081","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"finite_samples\",\"scale\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_samples, 7, ratios_equal_1/2_for_n<=7_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)","explanation_zh":"Wave6第十一層核對=(finite_samples, 7, ratios_equal_1/2_for_n<=7_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172081,"parameters":{"mode":"finite_samples","scale":7,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"finite_samples\",scale:7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0082","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"missing_limit\",\"scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(missing_limit, 8, absolute_ratios_alternate_between_1/9_and_9, limit_does_not_exist, 否)","explanation_zh":"Wave6第十一層核對=(missing_limit, 8, absolute_ratios_alternate_between_1/9_and_9, limit_does_not_exist, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172082,"parameters":{"mode":"missing_limit","scale":8,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"missing_limit\",scale:8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0083","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"signed_without_absolute\",\"scale\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_without_absolute, 9, a_n=(-1)^n*9*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)","explanation_zh":"Wave6第十一層核對=(signed_without_absolute, 9, a_n=(-1)^n*9*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172083,"parameters":{"mode":"signed_without_absolute","scale":9,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"signed_without_absolute\",scale:9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0084","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 10, a_n=10_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 10, a_n=10_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172084,"parameters":{"mode":"zero_terms","scale":10,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0085","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"finite_samples\",\"scale\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_samples, 11, ratios_equal_1/2_for_n<=11_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)","explanation_zh":"Wave6第十一層核對=(finite_samples, 11, ratios_equal_1/2_for_n<=11_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172085,"parameters":{"mode":"finite_samples","scale":11,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"finite_samples\",scale:11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0086","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"missing_limit\",\"scale\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(missing_limit, 12, absolute_ratios_alternate_between_1/13_and_13, limit_does_not_exist, 否)","explanation_zh":"Wave6第十一層核對=(missing_limit, 12, absolute_ratios_alternate_between_1/13_and_13, limit_does_not_exist, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172086,"parameters":{"mode":"missing_limit","scale":12,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"missing_limit\",scale:12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0087","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"signed_without_absolute\",\"scale\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_without_absolute, 13, a_n=(-1)^n*13*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)","explanation_zh":"Wave6第十一層核對=(signed_without_absolute, 13, a_n=(-1)^n*13*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172087,"parameters":{"mode":"signed_without_absolute","scale":13,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"signed_without_absolute\",scale:13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0088","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 14, a_n=14_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 14, a_n=14_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172088,"parameters":{"mode":"zero_terms","scale":14,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0089","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"finite_samples\",\"scale\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_samples, 15, ratios_equal_1/2_for_n<=15_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)","explanation_zh":"Wave6第十一層核對=(finite_samples, 15, ratios_equal_1/2_for_n<=15_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172089,"parameters":{"mode":"finite_samples","scale":15,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"finite_samples\",scale:15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0090","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"missing_limit\",\"scale\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(missing_limit, 16, absolute_ratios_alternate_between_1/17_and_17, limit_does_not_exist, 否)","explanation_zh":"Wave6第十一層核對=(missing_limit, 16, absolute_ratios_alternate_between_1/17_and_17, limit_does_not_exist, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172090,"parameters":{"mode":"missing_limit","scale":16,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"missing_limit\",scale:16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0091","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"signed_without_absolute\",\"scale\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_without_absolute, 17, a_n=(-1)^n*17*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)","explanation_zh":"Wave6第十一層核對=(signed_without_absolute, 17, a_n=(-1)^n*17*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172091,"parameters":{"mode":"signed_without_absolute","scale":17,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"signed_without_absolute\",scale:17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0092","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 18, a_n=18_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 18, a_n=18_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172092,"parameters":{"mode":"zero_terms","scale":18,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0093","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"finite_samples\",\"scale\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_samples, 19, ratios_equal_1/2_for_n<=19_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)","explanation_zh":"Wave6第十一層核對=(finite_samples, 19, ratios_equal_1/2_for_n<=19_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172093,"parameters":{"mode":"finite_samples","scale":19,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"finite_samples\",scale:19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0094","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"missing_limit\",\"scale\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(missing_limit, 20, absolute_ratios_alternate_between_1/21_and_21, limit_does_not_exist, 否)","explanation_zh":"Wave6第十一層核對=(missing_limit, 20, absolute_ratios_alternate_between_1/21_and_21, limit_does_not_exist, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172094,"parameters":{"mode":"missing_limit","scale":20,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"missing_limit\",scale:20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0095","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"signed_without_absolute\",\"scale\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_without_absolute, 21, a_n=(-1)^n*21*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)","explanation_zh":"Wave6第十一層核對=(signed_without_absolute, 21, a_n=(-1)^n*21*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172095,"parameters":{"mode":"signed_without_absolute","scale":21,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"signed_without_absolute\",scale:21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0096","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 22, a_n=22_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 22, a_n=22_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172096,"parameters":{"mode":"zero_terms","scale":22,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0097","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"finite_samples\",\"scale\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_samples, 23, ratios_equal_1/2_for_n<=23_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)","explanation_zh":"Wave6第十一層核對=(finite_samples, 23, ratios_equal_1/2_for_n<=23_then_equal_2, finite_prefix_cannot_determine_ratio_limit, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172097,"parameters":{"mode":"finite_samples","scale":23,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"finite_samples\",scale:23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0098","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"missing_limit\",\"scale\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(missing_limit, 24, absolute_ratios_alternate_between_1/25_and_25, limit_does_not_exist, 否)","explanation_zh":"Wave6第十一層核對=(missing_limit, 24, absolute_ratios_alternate_between_1/25_and_25, limit_does_not_exist, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172098,"parameters":{"mode":"missing_limit","scale":24,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"missing_limit\",scale:24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0099","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"signed_without_absolute\",\"scale\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_without_absolute, 25, a_n=(-1)^n*25*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)","explanation_zh":"Wave6第十一層核對=(signed_without_absolute, 25, a_n=(-1)^n*25*(1/2)^n, raw_ratio=-1/2_but_absolute_ratio=1/2, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172099,"parameters":{"mode":"signed_without_absolute","scale":25,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"signed_without_absolute\",scale:25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r02-ratio-test-series-0100","batch_id":"batch-20261015-advance-20261117-r02-ratio-test-series-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-test-series"],"title_zh":"級數比值判別法","stem_zh":"eventually nonzero、absolute successive ratio與limit存在責任。操作=ratio-test-boundary；資料={\"mode\":\"zero_terms\",\"scale\":26}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_terms, 26, a_n=26_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)","explanation_zh":"Wave6第十一層核對=(zero_terms, 26, a_n=26_for_odd_n_and_0_for_even_n, successive_ratio_has_zero_denominators_infinitely_often, 否)；依完整明示資料獨立重算；L<1絕對收斂、L>1發散、L=1無結論；有限ratio samples、zero denominators或raw signed ratio不能冒充假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比值判別法"]},"variant":{"family_id":"qf-mod48-ratio-test-boundary","seed":202611172100,"parameters":{"mode":"zero_terms","scale":26,"domain":"Exact_ratio_test_series","operation":"ratio-test-boundary","semantic_template":"ratio-test-boundary|{mode:\"zero_terms\",scale:26}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}