Abel criteria
Submitted by Structure on Sat, 11/01/2008 - 08:08.
Let
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a series where ,
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and has partial sum
equal bounded. Then
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We shall prove the convergence using Cauchy criteria
For there is a
such as
and
we have
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We have and as
are equal bounded there is a constant M such as
We can write
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if n is such as
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Using this criteria we have the convergence of a series
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and
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for all and