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: 42

Answer

Radius of convergence is $\sqrt R$

Work Step by Step

Let $x^{2}=y$., then $\sum_{n=1}^{\infty}c_{n}x^{2n}=\sum_{n=1}^{\infty}c_{n}y^{n}$ So it is convergent for $-R\lt y\lt R$ , therefore, for $x$ it is convergent of $-\sqrt R\lt x\lt \sqrt R$ Hence, Radius of convergence is $\sqrt R$
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