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R0034-17727 · q-20261014-advance-20261103-r03-infinite-series-0002
Use the ordered explicit rational terms=[1/3, -1/4]. Give (terms,partial_sum,count,finite_partial_sum_only), reducing the supplied term values and computed finite sum exactly.
G001 — Use the ordered explicit rational terms=[1/3, -1/4]. Give (terms,partial_sum,count,finite_partial_sum_only), reducing the supplied term values and computed finite sum exactly.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
ordered finite series partial sum := sum(1/3, -1/4)
After
ordered finite series partial sum = 1/12
Conditions: none
Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions.
Rule: exact_rational_arithmetic · Uses: G001
Before
original ordered reduced terms=[1/3, -1/4];term count=2
After
exact FINITE sum=1/12;finite_partial_sum_only
Conditions: none
Sum only the listed terms;the empty list has sum0.No unspecified continuation has been supplied,so this is not an infinite-series sum.
Rule: series_finite_terms_no_unspecified_infinite_continuation · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Recompute ordered finite series partial sum with exact rational arithmetic, not rounded decimals.([1/3, -1/4], 1/12, 2, finite_partial_sum_only)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 3db1a91af951a04759d19411366dc890e98bef2b4385b1099389b7a74c3d3c2bcandidate record SHA-256: f8d3541920637d0b83590a5534953597d341ad46a0dc5eff0743b74c56da91b8semantic review receipt SHA-256: f73d099ebe3ff1c69a5d96f08c75b11b9e5b05120af40cf3ef388fce3b5c5336question-first witness SHA-256: 22675ffb6209b4fea076032b29b96e3dc19aad4244c54493f5f65f5e5d875699Lean: NOT_RUN · human review: NOT_PERFORMED