CALCULUS Understanding Its Concepts and Methods

Radius of convergence

The radius of convergence of a power
seriesis
0
if the series diverges for all nonzero
*x*.

It is ∞ if the series converges absolutely for all
*x*.

Otherwise, it is the positive number *r*
such that the series converges absolutely for
|* x *| < *
r*
and diverges for
|* x *|
> *r*.

The radius of convergence is equal to , if that limit exists.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.