# Abel criteria

Submitted by Structure on Sat, 11/01/2008 - 08:08.

Let

a series where ,

and has partial sum equal bounded. Then

We shall prove the convergence using Cauchy criteria

For there is a such as and we have

We have and as are equal bounded there is a constant M such as

We can write

if n is such as

Using this criteria we have the convergence of a series

and

for all and