Calculus: Early Transcendentals 8th Edition

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

Chapter 11 - Review - True-False Quiz: 2

Answer

false

Work Step by Step

Given:$ \sum_{n=1}^{\infty}{n^{-sin1}}$ or $ \sum_{n=1}^{\infty}\frac{1}{n^{sin1}}$ Any series of the form $ \sum_{n=1}^{\infty}\frac{1}{n^{p}}$ is known as p-series. A p-series is convergent if and only if $p>1$ Here $p=sin1$ and $sin1<1$ Thus, the series diverges. Hence, the statement is false.
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