Which statement correctly identifies when an infinite geometric series converges?

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Which statement correctly identifies when an infinite geometric series ∑n=0∞arn\sum_{n=0}^{\infty} ar^{n} converges? (a) It converges if and only if 0<r<10<r<1. (b) It converges whenever ∣r∣>1|r|>1. (c) It converges if and only if ∣r∣<1|r|<1. (d) It converges if and only if −1≤r≤1-1\le r\le 1.

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