Which condition on the common ratio guarantees that the infinite geometric series…

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

Problem

Which condition on the common ratio rr guarantees that the infinite geometric series ∑k=0∞ark\displaystyle \sum_{k=0}^{\infty} ar^{k} converges to a finite value? (a) r<1r<1 (b) ∣r∣<1|r|<1 (c) ∣r∣≤1|r|\le1 (d) ∣ar∣<1|a r|<1

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