Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 9 - Infinite Series - 9.2 Exercises - Page 602: 57

Answer

Please see step-by-step

Work Step by Step

The series $\displaystyle \sum_{n=0}^{\infty}ar^{n}=a+ar+ar^{2}+\cdots+ar^{n}+\cdots,\ a\neq 0$ is a geometric series with ratio $r$. By Th.9.6, When $0 \lt |r| \lt 1$, the series converges to $\displaystyle \frac{a}{1-r}$. When $|r|\geq 1$, the series diverges.
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