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 792: 39

Answer

$R=\frac{1}{c}$

Work Step by Step

$\lim\limits_{n \to \infty} \sqrt[n] {|c_{n}x^{n}|}=|x|\lim\limits_{n \to \infty} \sqrt[n] {|c_{n}|}$ $=c|x|\lt 1$ for convergence, or $|x|\lt 1/c $ so we will get $R=\frac{1}{c}$
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