Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - 11.2 Series - 11.2 Exercises - Page 756: 22

Answer

The series converges and its sum is $\frac{5}{\pi-1}$. Now To reach that we observe that the intial term is $\frac{5}{\pi}$ and the common ration |$r$| = $\frac{1}{\pi} \lt 1 $ . And Such case according to definition 4 in page 750: $S= \frac{a}{1-r}$ = $\frac{\frac{5}{\pi}}{1-\frac{1}{\pi}} = \frac{5}{\pi-1} $

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