Series, Convergence, and Series Tests

• Return to the Sequences and Series starting page
• The formal definition of a series
• Some common series
• A list of series tests
• Using series tests to determine convergence

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

and .

• Return to the Sequences and Series starting page
• The formal definition of a series
• Some common series
• A list of series tests
• Using series tests to determine convergence

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