Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.5 The Ratio and Root Tests and Strategies for Choosing Tests - Exercises - Page 568: 40


The root test is inconclusive.

Work Step by Step

To apply the root test, we have $$ L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{(1+(1/n))^{-n})}\\ =\lim _{n \rightarrow \infty} \frac{1}{(1+(1/n))}=1 $$ Hence the root test is inconclusive.
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