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: 9


$R=4$ and interval of convergence $[-4,4]$

Work Step by Step

Given: $a_{n}=\frac{x^{n}}{(n)^44^{n}}$ $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{x^{n+1}}{(n+1)^44^{n+1}}}{\frac{x^{n}}{(n)^44^{n}}}|=\frac{|x|}{4}$ Hence, $R=4$ and interval of convergence $[-4,4]$
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