Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.8 - Power Series - 11.8 Exercises - Page 751: 12


$R=5$ ; the interval of convergence is $(-5,5]$

Work Step by Step

$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{x^{n+1}}{(n+1)5^{n+1}}}{\frac{x^n}{n5^ n}}|$ $=\frac{|x|}{5}$ Hence, $R=5$ ; the interval of convergence is $(-5,5]$
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