Use a_n=(1/2)^n for every n≥0, positive ratio q=1/2, and center c=-12. Give (coefficient_law, center, radius, interior_status, exterior_status, boundary).
G001 — Use a_n=(1/2)^n for every n≥0, positive ratio q=1/2, and center c=-12. Give (coefficient_law, center, radius, interior_status, exterior_status, boundary).
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.
source operation=radius-geometric-exact;original snapshot and mathematics retained
After
explicit ordered source output fields=[coefficient_law, center, radius, interior_status, exterior_status, boundary]
Conditions: none
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 WHOLE a_n=(1/2)^n for EVERY n>=0;center=-12;positive q=1/2
After
absolute geometric term ratio=q*|x-center|;less than1 gives absolute convergence,greater than1 makes terms not tend0;exact radius1/q=2
Conditions: none
Use the law for every n,not a handful of coefficients.Keep interior and exterior separate and audit endpoints separately;a radius does not replace endpoint conclusions.
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.