Mathematics

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}