Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.7 Strategy for Testing Series - 11.7 Exercises - Page 786: 37



Work Step by Step

$\lim\limits_{n \to \infty} \sqrt[n] a_{n}=\lim\limits_{n \to \infty} \sqrt[n] {(\sqrt[n] {2-1)^{n}}}$ $=\lim\limits_{n \to \infty}(\sqrt[n] 2-1)$ $=\lim\limits_{n \to \infty}( 2^{1/n}-1)$ $=1-1$ $=0$ The series is convergent.
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