Question 17743: A Finite Partial Sum Is Not an Infinite-Series Limit

Original question and givens

Use the ordered explicit rational terms=[1/19, -1/20]. 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=[1/19, -1/20]. 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

Step-by-step derivation

ordered finite series partial sum := sum(1/19, -1/20)

ordered finite series partial sum = 1/380

original ordered reduced terms=[1/19, -1/20];term count=2

exact FINITE sum=1/380;finite_partial_sum_only

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

([1/19, -1/20], 1/380, 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.