CALCULUS Understanding Its Concepts and Methods
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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:
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Lagrange form of the remainder
Radius of convergence
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.