# Question 17735: A Finite Partial Sum Is Not an Infinite-Series Limit

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0034-17735 · q-20261014-advance-20261103-r03-infinite-series-0010



## Original question and givens

Use the ordered explicit rational terms=[1/11, -1/12]. 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=[1/11, -1/12]. Give (terms,partial_sum,count,finite_partial_sum_only), reducing the supplied term values and computed finite sum exactly.





## Definition and scope

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.


- [mko-infinite-series](https://ocme.evemisslab.com/en/mko/mko-infinite-series/)





## Step-by-step derivation

S001 · calculationBefore

ordered finite series partial sum := sum(1/11, -1/12)

After

ordered finite series partial sum = 1/132

Conditions: none

Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001





S002 · impliesBefore

original ordered reduced terms=[1/11, -1/12];term count=2

After

exact FINITE sum=1/132;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.

Step identifiers and dependenciesRule: series_finite_terms_no_unspecified_infinite_continuation · Uses: G001, S001









## Reverse checks


- 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.





## Result

([1/11, -1/12], 1/132, 2, finite_partial_sum_only)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: 54d1166229b260e8e4e30732d2d15797433a7719219bc0f103d4dcb6c9460124
- candidate record SHA-256: feb03e0d9526990dd3f2cc88fb8f564d6fb6dd1c62ae6aff0ad09307c28f3c52
- semantic review receipt SHA-256: f73d099ebe3ff1c69a5d96f08c75b11b9e5b05120af40cf3ef388fce3b5c5336
- question-first witness SHA-256: 22675ffb6209b4fea076032b29b96e3dc19aad4244c54493f5f65f5e5d875699
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261103-r03-infinite-series-0010.json)