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Infinite series, Partial sums, Convergent series

An expression of the formMATHin 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 MATHThe numbers $s_{n}$ make perfectly good sense. We then examine the sequence MATH to see if it converges.

If the sequence $s_{n}$ converges to $L$, then we say that the infinite series MATH sums (or converges) to $L$. 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

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Absolutely convergent series

Conditionally convergent series

Geometric series

Harmonic series

p-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.

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