CALCULUS Understanding Its Concepts and Methods
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Infinite series, Partial sums, Convergent series
An expression of the formin which the last ellipsis indicates that the sum has no end, is called an infinite series.
Of course it is impossible to add an infinite number of terms. So what does such an expression mean? The basic idea is to look at the sequence of partial sums The numbers make perfectly good sense. We then examine the sequence to see if it converges.
If the sequence converges to , then we say that the infinite series sums (or converges) to . An infinite series that does not converge is said to diverge.
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
Absolutely convergent series
Conditionally convergent series
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.