Series, Convergence, and Series Tests

You may recall, from back when you first started studying integration, that you approximated the area under a curve by adding up a bunch of rectangles.

[a curve with rectangles
under it]

You then made the width of the rectangles smaller and smaller, finding the limit of the area as the width went to zero, to find the area. In a sense, you were adding up an infinite number of rectangle areas. Series are a way to formally add up an an infinite amount of numbers, in a way that makes sense. However, determining whether or not the series you are looking at converges, that is, whether or not it has a real sum, can be tricky. In addition to some basic information on series, these pages should be able to help you determine whether or not your series converges.

In this set of pages, the series of interest will always by symbolized as the sum, as n goes from 1 to infinity, of a[n]. In addition, any auxilliary sequence will be symbolized as the sum, as n goes from 1 to infinity, of b[n]. Symbolically, that is

[sum notation] and [more sum notation].

Copyright © 1996 Department of Mathematics, Oregon State University

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