Use mode=zero_radius, positive scale=1, source prefix_length=0, first_ratio=1, second_ratio=1. zero_radius/infinite_radius require the canonical unused-field sentinels prefix0 and ratios1. Give (mode, scale, coefficient_law, radius, symbolic_certificate, certificate).
G001 — Use mode=zero_radius, positive scale=1, source prefix_length=0, first_ratio=1, second_ratio=1. zero_radius/infinite_radius require the canonical unused-field sentinels prefix0 and ratios1. Give (mode, scale, coefficient_law, radius, symbolic_certificate, certificate).
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.
Keep the source snapshot while listing ordered fields without JavaScript.Radius uses its original mode to select6 or11 fields without padding;distinguish nonclaims from actual negations.
ORIGINAL mode=zero_radius,positive scale=1;unused-field sentinels prefix0,ratios1/1
After
WHOLE a_n=scale*n! for EVERY n>=0;for any nonzero displacement t,absolute term ratio=|t|*(n+1) grows without bound,so terms cannot tend0;at t0 the series is finite,thus R0
Conditions: none
Radius0 is legal and does not mean divergence at the center.Nonzero scale and the whole factorial law control all later terms,not a finite prefix.
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.