For real numbers and

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

For real numbers

a

and

r\,(r\neq0)

, consider the infinite series

\displaystyle\sum_{n=0}^{\infty} ar^{n}

. Which condition on

r

guarantees that this series converges? (a)

r<1

(b)

|r|\le 1

(c)

|r|<1

(d)

r>-1