CALCULUS Understanding Its Concepts and Methods

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

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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.