Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.3 Infinite Series - 8.3 Exercises - Page 623: 37


$=\dfrac {\pi }{\pi +1}$

Work Step by Step

$3\sum ^{\infty }_{k=0}\left( -\pi \right) ^{-k}=3\sum ^{\infty }_{k=0}\left( -\dfrac {1}{\pi }\right) ^{k}=3\dfrac {a_{1}}{1-r};a_{1}=\left( -\dfrac {1}{\pi }\right) ^{0}=1;r=-\dfrac {1}{\pi }\Rightarrow S_{\infty }=\dfrac {a_{1}}{1-r}=\dfrac {1}{1-\left( -\dfrac {1}{\pi }\right) }=\dfrac {\pi }{\pi +1}$
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