Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - Review - Exercises - Page 825: 17



Work Step by Step

The Comparison Test: $|cosx|\leq 1$ for all $x$ The geometric series $\Sigma_{n=1}^\infty r^{n}$ is convergent if $|r|\lt 1$ and divergent if $|r|\geq 1$ $|a_{n}|=\frac{|cos3n|}{1+(1.2)^{n}}\leq \frac{1}{1+(1.2)^{n}} \lt \frac{1}{(1.2)^{n}}=\frac{1}{(1.2)^{n}}$ Since, $\Sigma_{n=1}^\infty\frac{1}{(1.2)^{n}}$ is convergent. Hence, $\Sigma_{n=1}^\infty|a_{n}|$ is convergent.
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