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: 11


$R=\frac{1}{4}$ and Interval of convergence: $(-\frac{1}{4},\frac{1}{4}]$

Work Step by Step

Given: $a_n=\frac{4^nx^n}{\sqrt n}$ Thus, $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{4^{n+1}x^{n+1}}{\sqrt {(n+1)}}}{\frac{4^nx^n}{\sqrt n}}|=4|x|$ Hence, $R=\frac{1}{4}$ and Interval of convergence: $(-\frac{1}{4},\frac{1}{4}]$
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