Question 7138: Five Prefix Sums and Four Ordered Differences

Original question and givens

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[0, 0, 0, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

• G001 — N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[0, 0, 0, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

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-sequence

Step-by-step derivation

N starts at0;ordered finite indices and repeated values retained

given recurrences differ from guessing an infinite rule from observations

finite prefix sum through0 := sum(0, 0)

finite prefix sum through0 = 0

finite prefix sum through1 := sum(0, 0)

finite prefix sum through1 = 0

finite prefix sum through2 := sum(0, 0)

finite prefix sum through2 = 0

finite prefix sum through3 := sum(0, -1)

finite prefix sum through3 = -1

finite prefix sum through4 := sum(-1, 1)

finite prefix sum through4 = 0

finite adjacent delta0 := sub(0, 0)

finite adjacent delta0 = 0

finite adjacent delta1 := sub(0, 0)

finite adjacent delta1 = 0

finite adjacent delta2 := sub(-1, 0)

finite adjacent delta2 = -1

finite adjacent delta3 := sub(1, -1)

finite adjacent delta3 = 2

[0, 0, 0, -1, 1]

all five values equal=No

Reverse checks

• S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S010 · premise_and_result_audit — Recompute finite adjacent delta3 with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute finite adjacent delta2 with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute finite adjacent delta1 with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute finite adjacent delta0 with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute finite prefix sum through4 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute finite prefix sum through3 with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute finite prefix sum through2 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute finite prefix sum through1 with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute finite prefix sum through0 with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([0, 0, 0, -1, 0], [0, 0, -1, 2], No)

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.