Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.3 Exercises - Page 745: 12

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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