Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.3 The Integral Test and Estimates of Sums - 11.3 Exercises - Page 766: 27

Answer

Function is neither positive nor decreasing.

Work Step by Step

Given: $\Sigma_{n=1}^{\infty}\frac{cos(\pi n)}{\sqrt n}$ The integral test requires a function that is positive and decreasing on $[1,\infty)$ . The $cos \pi n$ alternates between $-1$ and $+1$ , so it is not positive and decreasing for the entire interval. Hence, Function is neither positive nor decreasing.
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