CALCULUS Understanding Its Concepts and Methods

Interval of convergence

The interval of convergence of a power
seriesis
the set of real numbers
*x*
for which the power series converges. In the extreme cases it can consists of
just the single point
*p*,
or it can be the set of all real numbers. Normally, it is an interval with
endpoints *p*
- *r*
and
*p*
+ *r*
where
*r*
is the radius of convergence of the
series. This interval may or may not contain either of the endpoints. So there
are four possibilities for the
interval:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Lagrange form of the remainder

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.