# 級數絕對收斂基礎 · 脈衝 R03 本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。 本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。 batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations · 2026-10-14 · 100 題 欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。 [欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json) ## 1. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[1,2],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(1/2, -1/2, 1, 是, absolute_geometric_certificate) Wave5第四層核對=(1/2, -1/2, 1, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0001/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 2. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[2,3],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(2/3, -1/2, 4/3, 是, absolute_geometric_certificate) Wave5第四層核對=(2/3, -1/2, 4/3, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0002/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 3. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[3,4],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(3/4, -1/2, 3/2, 是, absolute_geometric_certificate) Wave5第四層核對=(3/4, -1/2, 3/2, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0003/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 4. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[4,5],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(4/5, -1/2, 8/5, 是, absolute_geometric_certificate) Wave5第四層核對=(4/5, -1/2, 8/5, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0004/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 5. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[5,6],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(5/6, -1/2, 5/3, 是, absolute_geometric_certificate) Wave5第四層核對=(5/6, -1/2, 5/3, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0005/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 6. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[6,7],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(6/7, -1/2, 12/7, 是, absolute_geometric_certificate) Wave5第四層核對=(6/7, -1/2, 12/7, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0006/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 7. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[7,8],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(7/8, -1/2, 7/4, 是, absolute_geometric_certificate) Wave5第四層核對=(7/8, -1/2, 7/4, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0007/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 8. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[8,9],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(8/9, -1/2, 16/9, 是, absolute_geometric_certificate) Wave5第四層核對=(8/9, -1/2, 16/9, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0008/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 9. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[9,10],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(9/10, -1/2, 9/5, 是, absolute_geometric_certificate) Wave5第四層核對=(9/10, -1/2, 9/5, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0009/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 10. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[10,11],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(10/11, -1/2, 20/11, 是, absolute_geometric_certificate) Wave5第四層核對=(10/11, -1/2, 20/11, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0010/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 11. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[11,12],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(11/12, -1/2, 11/6, 是, absolute_geometric_certificate) Wave5第四層核對=(11/12, -1/2, 11/6, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0011/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 12. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[12,13],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(12/13, -1/2, 24/13, 是, absolute_geometric_certificate) Wave5第四層核對=(12/13, -1/2, 24/13, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0012/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 13. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[13,14],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(13/14, -1/2, 13/7, 是, absolute_geometric_certificate) Wave5第四層核對=(13/14, -1/2, 13/7, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0013/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 14. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[14,15],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(14/15, -1/2, 28/15, 是, absolute_geometric_certificate) Wave5第四層核對=(14/15, -1/2, 28/15, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0014/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 15. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[15,16],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(15/16, -1/2, 15/8, 是, absolute_geometric_certificate) Wave5第四層核對=(15/16, -1/2, 15/8, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0015/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 16. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[16,17],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(16/17, -1/2, 32/17, 是, absolute_geometric_certificate) Wave5第四層核對=(16/17, -1/2, 32/17, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0016/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 17. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[17,18],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(17/18, -1/2, 17/9, 是, absolute_geometric_certificate) Wave5第四層核對=(17/18, -1/2, 17/9, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0017/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 18. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[18,19],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(18/19, -1/2, 36/19, 是, absolute_geometric_certificate) Wave5第四層核對=(18/19, -1/2, 36/19, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0018/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 19. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[19,20],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(19/20, -1/2, 19/10, 是, absolute_geometric_certificate) Wave5第四層核對=(19/20, -1/2, 19/10, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0019/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 20. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[20,21],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(20/21, -1/2, 40/21, 是, absolute_geometric_certificate) Wave5第四層核對=(20/21, -1/2, 40/21, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0020/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 21. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[21,22],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(21/22, -1/2, 21/11, 是, absolute_geometric_certificate) Wave5第四層核對=(21/22, -1/2, 21/11, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0021/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 22. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[22,23],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(22/23, -1/2, 44/23, 是, absolute_geometric_certificate) Wave5第四層核對=(22/23, -1/2, 44/23, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0022/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 23. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[23,24],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(23/24, -1/2, 23/12, 是, absolute_geometric_certificate) Wave5第四層核對=(23/24, -1/2, 23/12, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0023/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 24. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[24,25],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(24/25, -1/2, 48/25, 是, absolute_geometric_certificate) Wave5第四層核對=(24/25, -1/2, 48/25, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0024/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 25. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={"a":[25,26],"r":[-1,2]}。請依 [a, r, absolute_series_sum, absolutely_convergent, certificate] 欄序回答。 查看答案與解釋(25/26, -1/2, 25/13, 是, absolute_geometric_certificate) Wave5第四層核對=(25/26, -1/2, 25/13, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0025/) 級數絕對收斂 · qf-mod35-absseries-geometric · candidate ## 26. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":1,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(1, 5, [1, -1/2, 1/3, -1/4, 1/5], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(1, 5, [1, -1/2, 1/3, -1/4, 1/5], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0026/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 27. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":2,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(2, 5, [1/2, -1/3, 1/4, -1/5, 1/6], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(2, 5, [1/2, -1/3, 1/4, -1/5, 1/6], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0027/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 28. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":3,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(3, 5, [1/3, -1/4, 1/5, -1/6, 1/7], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(3, 5, [1/3, -1/4, 1/5, -1/6, 1/7], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0028/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 29. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":4,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(4, 5, [1/4, -1/5, 1/6, -1/7, 1/8], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(4, 5, [1/4, -1/5, 1/6, -1/7, 1/8], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0029/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 30. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":5,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0030/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 31. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":6,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(6, 5, [1/6, -1/7, 1/8, -1/9, 1/10], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(6, 5, [1/6, -1/7, 1/8, -1/9, 1/10], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0031/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 32. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":7,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(7, 5, [1/7, -1/8, 1/9, -1/10, 1/11], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(7, 5, [1/7, -1/8, 1/9, -1/10, 1/11], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0032/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 33. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":8,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(8, 5, [1/8, -1/9, 1/10, -1/11, 1/12], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(8, 5, [1/8, -1/9, 1/10, -1/11, 1/12], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0033/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 34. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":9,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(9, 5, [1/9, -1/10, 1/11, -1/12, 1/13], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(9, 5, [1/9, -1/10, 1/11, -1/12, 1/13], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0034/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 35. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":10,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(10, 5, [1/10, -1/11, 1/12, -1/13, 1/14], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(10, 5, [1/10, -1/11, 1/12, -1/13, 1/14], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0035/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 36. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":11,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(11, 5, [1/11, -1/12, 1/13, -1/14, 1/15], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(11, 5, [1/11, -1/12, 1/13, -1/14, 1/15], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0036/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 37. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":12,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(12, 5, [1/12, -1/13, 1/14, -1/15, 1/16], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(12, 5, [1/12, -1/13, 1/14, -1/15, 1/16], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0037/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 38. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":13,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(13, 5, [1/13, -1/14, 1/15, -1/16, 1/17], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(13, 5, [1/13, -1/14, 1/15, -1/16, 1/17], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0038/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 39. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":14,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(14, 5, [1/14, -1/15, 1/16, -1/17, 1/18], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(14, 5, [1/14, -1/15, 1/16, -1/17, 1/18], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0039/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 40. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":15,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(15, 5, [1/15, -1/16, 1/17, -1/18, 1/19], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(15, 5, [1/15, -1/16, 1/17, -1/18, 1/19], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0040/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 41. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":16,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(16, 5, [1/16, -1/17, 1/18, -1/19, 1/20], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(16, 5, [1/16, -1/17, 1/18, -1/19, 1/20], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0041/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 42. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":17,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(17, 5, [1/17, -1/18, 1/19, -1/20, 1/21], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(17, 5, [1/17, -1/18, 1/19, -1/20, 1/21], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0042/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 43. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":18,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(18, 5, [1/18, -1/19, 1/20, -1/21, 1/22], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(18, 5, [1/18, -1/19, 1/20, -1/21, 1/22], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0043/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 44. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":19,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(19, 5, [1/19, -1/20, 1/21, -1/22, 1/23], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(19, 5, [1/19, -1/20, 1/21, -1/22, 1/23], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0044/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 45. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":20,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(20, 5, [1/20, -1/21, 1/22, -1/23, 1/24], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(20, 5, [1/20, -1/21, 1/22, -1/23, 1/24], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0045/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 46. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":21,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(21, 5, [1/21, -1/22, 1/23, -1/24, 1/25], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(21, 5, [1/21, -1/22, 1/23, -1/24, 1/25], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0046/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 47. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":22,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(22, 5, [1/22, -1/23, 1/24, -1/25, 1/26], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(22, 5, [1/22, -1/23, 1/24, -1/25, 1/26], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0047/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 48. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":23,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(23, 5, [1/23, -1/24, 1/25, -1/26, 1/27], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(23, 5, [1/23, -1/24, 1/25, -1/26, 1/27], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0048/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 49. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":24,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(24, 5, [1/24, -1/25, 1/26, -1/27, 1/28], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(24, 5, [1/24, -1/25, 1/26, -1/27, 1/28], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0049/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 50. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={"shift":25,"n":5}。請依 [shift, n, terms, series_converges, absolutely_converges, certificate] 欄序回答。 查看答案與解釋(25, 5, [1/25, -1/26, 1/27, -1/28, 1/29], 是, 否, alternating_remainder_and_harmonic_absolute_divergence) Wave5第四層核對=(25, 5, [1/25, -1/26, 1/27, -1/28, 1/29], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0050/) 級數絕對收斂 · qf-mod35-absseries-conditional-alternating · candidate ## 51. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,2],[-1,3]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/2, -1/3], [1/2, 1/3], 5/6, finite_absolute_partial_sum_only) Wave5第四層核對=([1/2, -1/3], [1/2, 1/3], 5/6, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0051/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 52. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,3],[-1,4]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/3, -1/4], [1/3, 1/4], 7/12, finite_absolute_partial_sum_only) Wave5第四層核對=([1/3, -1/4], [1/3, 1/4], 7/12, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0052/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 53. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,4],[-1,5]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/4, -1/5], [1/4, 1/5], 9/20, finite_absolute_partial_sum_only) Wave5第四層核對=([1/4, -1/5], [1/4, 1/5], 9/20, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0053/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 54. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,5],[-1,6]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/5, -1/6], [1/5, 1/6], 11/30, finite_absolute_partial_sum_only) Wave5第四層核對=([1/5, -1/6], [1/5, 1/6], 11/30, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0054/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 55. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,6],[-1,7]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/6, -1/7], [1/6, 1/7], 13/42, finite_absolute_partial_sum_only) Wave5第四層核對=([1/6, -1/7], [1/6, 1/7], 13/42, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0055/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 56. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,7],[-1,8]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/7, -1/8], [1/7, 1/8], 15/56, finite_absolute_partial_sum_only) Wave5第四層核對=([1/7, -1/8], [1/7, 1/8], 15/56, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0056/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 57. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,8],[-1,9]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/8, -1/9], [1/8, 1/9], 17/72, finite_absolute_partial_sum_only) Wave5第四層核對=([1/8, -1/9], [1/8, 1/9], 17/72, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0057/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 58. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,9],[-1,10]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/9, -1/10], [1/9, 1/10], 19/90, finite_absolute_partial_sum_only) Wave5第四層核對=([1/9, -1/10], [1/9, 1/10], 19/90, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0058/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 59. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,10],[-1,11]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/10, -1/11], [1/10, 1/11], 21/110, finite_absolute_partial_sum_only) Wave5第四層核對=([1/10, -1/11], [1/10, 1/11], 21/110, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0059/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 60. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,11],[-1,12]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/11, -1/12], [1/11, 1/12], 23/132, finite_absolute_partial_sum_only) Wave5第四層核對=([1/11, -1/12], [1/11, 1/12], 23/132, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0060/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 61. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,12],[-1,13]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/12, -1/13], [1/12, 1/13], 25/156, finite_absolute_partial_sum_only) Wave5第四層核對=([1/12, -1/13], [1/12, 1/13], 25/156, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0061/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 62. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,13],[-1,14]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/13, -1/14], [1/13, 1/14], 27/182, finite_absolute_partial_sum_only) Wave5第四層核對=([1/13, -1/14], [1/13, 1/14], 27/182, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0062/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 63. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,14],[-1,15]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/14, -1/15], [1/14, 1/15], 29/210, finite_absolute_partial_sum_only) Wave5第四層核對=([1/14, -1/15], [1/14, 1/15], 29/210, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0063/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 64. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,15],[-1,16]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/15, -1/16], [1/15, 1/16], 31/240, finite_absolute_partial_sum_only) Wave5第四層核對=([1/15, -1/16], [1/15, 1/16], 31/240, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0064/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 65. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,16],[-1,17]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/16, -1/17], [1/16, 1/17], 33/272, finite_absolute_partial_sum_only) Wave5第四層核對=([1/16, -1/17], [1/16, 1/17], 33/272, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0065/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 66. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,17],[-1,18]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/17, -1/18], [1/17, 1/18], 35/306, finite_absolute_partial_sum_only) Wave5第四層核對=([1/17, -1/18], [1/17, 1/18], 35/306, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0066/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 67. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,18],[-1,19]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/18, -1/19], [1/18, 1/19], 37/342, finite_absolute_partial_sum_only) Wave5第四層核對=([1/18, -1/19], [1/18, 1/19], 37/342, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0067/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 68. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,19],[-1,20]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/19, -1/20], [1/19, 1/20], 39/380, finite_absolute_partial_sum_only) Wave5第四層核對=([1/19, -1/20], [1/19, 1/20], 39/380, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0068/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 69. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,20],[-1,21]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/20, -1/21], [1/20, 1/21], 41/420, finite_absolute_partial_sum_only) Wave5第四層核對=([1/20, -1/21], [1/20, 1/21], 41/420, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0069/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 70. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,21],[-1,22]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/21, -1/22], [1/21, 1/22], 43/462, finite_absolute_partial_sum_only) Wave5第四層核對=([1/21, -1/22], [1/21, 1/22], 43/462, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0070/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 71. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,22],[-1,23]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/22, -1/23], [1/22, 1/23], 45/506, finite_absolute_partial_sum_only) Wave5第四層核對=([1/22, -1/23], [1/22, 1/23], 45/506, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0071/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 72. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,23],[-1,24]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/23, -1/24], [1/23, 1/24], 47/552, finite_absolute_partial_sum_only) Wave5第四層核對=([1/23, -1/24], [1/23, 1/24], 47/552, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0072/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 73. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,24],[-1,25]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/24, -1/25], [1/24, 1/25], 49/600, finite_absolute_partial_sum_only) Wave5第四層核對=([1/24, -1/25], [1/24, 1/25], 49/600, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0073/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 74. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,25],[-1,26]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/25, -1/26], [1/25, 1/26], 51/650, finite_absolute_partial_sum_only) Wave5第四層核對=([1/25, -1/26], [1/25, 1/26], 51/650, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0074/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 75. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={"terms":[[1,26],[-1,27]]}。請依 [terms, absolute_terms, absolute_partial_sum, boundary] 欄序回答。 查看答案與解釋([1/26, -1/27], [1/26, 1/27], 53/702, finite_absolute_partial_sum_only) Wave5第四層核對=([1/26, -1/27], [1/26, 1/27], 53/702, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0075/) 級數絕對收斂 · qf-mod35-absseries-absolute-partial · candidate ## 76. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":1,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(1, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(1, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0076/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 77. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":2,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(2, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(2, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0077/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 78. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":3,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(3, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(3, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0078/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 79. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":4,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(4, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(4, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0079/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 80. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":5,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(5, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(5, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0080/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 81. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":6,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(6, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(6, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0081/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 82. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":7,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(7, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(7, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0082/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 83. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":8,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(8, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(8, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0083/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 84. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":9,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(9, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(9, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0084/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 85. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":10,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(10, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(10, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0085/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 86. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":11,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(11, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(11, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0086/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 87. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":12,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(12, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(12, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0087/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 88. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":13,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(13, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(13, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0088/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 89. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":14,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(14, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(14, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0089/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 90. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":15,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(15, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(15, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0090/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 91. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":16,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(16, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(16, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0091/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 92. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":17,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(17, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(17, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0092/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 93. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":18,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(18, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(18, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0093/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 94. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":19,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(19, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(19, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0094/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 95. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":20,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(20, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(20, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0095/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 96. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":21,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(21, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(21, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0096/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 97. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":22,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(22, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(22, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0097/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 98. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":23,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(23, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(23, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0098/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 99. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":24,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(24, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(24, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0099/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate ## 100. 絕對收斂 partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={"shift":25,"prefix_length":5}。請依 [shift, prefix_length, terms_tend_to_zero, term_zero_suffices_for_absolute_convergence, boundary] 欄序回答。 查看答案與解釋(25, 5, 是, 否, term_zero_not_absolute_convergence) Wave5第四層核對=(25, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261104-r03-absolute-convergence-of-series-0100/) 級數絕對收斂 · qf-mod35-absseries-term-zero-boundary · candidate [原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations/validation-report.json)