Abel's test

The criterion of Abel is a mathematical convergence criterion. It belongs to the group of direct criteria.

Abelian criterion for convergence

The series converges if is of finite variation and the series is convergent.

In the real case the demand that is monotonic and is in lieu of finite variation is sufficient.

Abelian criterion for uniform convergence

Be

And

In the area defined function consequences. is uniformly bounded, the consequences for every monotonic and the series

Uniformly convergent, then the series

Uniformly convergent.