Determine whether the series converges

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

Problem

Determine whether the series

\displaystyle \sum_{n=2}^{\infty} 5\left(\dfrac{3}{4}\right)^{n-2}

converges. If it converges, what is its sum? (a) It converges; the sum is

\dfrac{80}{3}

. (b) It diverges because the common ratio exceeds

1

in magnitude. (c) It converges; the sum is

20

. (d) It converges; the sum is

\dfrac{45}{4}