Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 22

Answer

Converges and sum is $S= \frac{5}{\pi-1} $

Work Step by Step

The series converges and its sum is $\frac{5}{\pi-1}$. We observe that the intial term is $\frac{5}{\pi}$ and the common ration |$r$| = $\frac{1}{\pi} \lt 1 $ . $S= \frac{a}{1-r}$ = $\frac{\frac{5}{\pi}}{1-\frac{1}{\pi}} = \frac{5}{\pi-1} $
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