CALCULUS Understanding Its Concepts and Methods

Sequence

An infinite sequence is a list that never ends.

Sequences are called infinite because they never stop---there is no last term.

If exists, then the sequence , , , , is said to converge. Otherwise, the sequence is said to diverge.

The statement means that as gets large, the difference between and gets arbitrarily small. No matter how large a positive integer you choose, the numbers in the sequence eventually get within of ; that is, there is a positive integer such that whenever .

The statement means that as gets large, the terms get arbitrarily large. No matter how large a positive integer you choose, there is a positive integer such that whenever .

The statement means that .

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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.