Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.7 Strategy for Testing Series - 11.7 Exercises - Page 786: 14

Answer

Convergent

Work Step by Step

$\sum\frac{sin2n}{1+2^{n}}\leq \sum \frac{1}{1+2^{n}}$ $\sum\frac{1}{1+2^{n}}\lt \sum \frac{1}{2^{n}}$ Here, $\sum \frac{1}{2^{n}}$ is a geometric series with common ratio $r=1/2$. Hence, the series is convergent.
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