Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.8 Power Series - 11.8 Exercises - Page 791: 12


$R=5$ and Interval of convergence is $(-5,5]$

Work Step by Step

Given: $a_n=\frac{x^n}{n5^ n}$ Thus, $\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\dfrac{x^{n+1}}{(n+1)5^{n+1}}}{\dfrac{x^n}{n5^ n}}|=\dfrac{|x|}{5}$ Hence, $R=5$ and Interval of convergence is $(-5,5]$
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