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: 14

Answer

Convergent

Work Step by Step

As a summation the series can be written as $\Sigma_{n=1}^{\infty}\frac{1}{n\sqrt n}=\Sigma_{n=1}^{\infty}\frac{1}{n^{3/2}}$, which is a convergent p-series with $p=\frac{3}{2}\gt 1$. Hence, the given series is convergent.
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