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Comparison test

A comparison test determines whether a series converges by comparing it to another series.

Comparison TestSuppose MATH for all $n$. Then

1.If $\sum b_{n}$ converges, then $\sum a_{n}$ converges.

2.If $\sum a_{n}$ diverges, then $\sum b_{n}$ diverges.

Limit Comparison TestSuppose $a_{n}>0$ and $b_{n}>0$ for all $n$, and thatMATHThen

1.If $0<L<\infty $, then $\sum a_{n}$ converges if and only if $\sum b_{n}$ converges.

2.If $L=0$, and $\sum b_{n}$ converges, then $\sum a_{n}$ converges.


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


Absolute convergence

Alternating series

Divergent series

Integral test

Limit comparison test

p-series

Ratio test


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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