Divergent series

In mathematics, a divergent series is a series that does not converge.

Related Topics:
Mathematics - Series

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If a series converges, the individual terms of the series must approach zero. Thus any series in which

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the individual terms do not approach zero diverges. The simplest example of a divergent series whose terms

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do approach zero is the harmonic series

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:1 + {1 over 2} + {1 over 3} + {1 over 4} + {1 over 5} + cdots =sum_{n=1}^inftyrac{1}{n}.

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Divergent series can sometimes be assigned a value by using a summability method.

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For example, Cesàro summation assigns the divergent series

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:1 - 1 + 1 - 1 + cdots

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the value rac{1}{2}.

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