Category:Examples of Absolutely Convergent Complex Series

This category contains examples of Absolutely Convergent Complex Series.

Let $S = \ds \sum_{n \mathop = 1}^\infty a_n$ be a series in the complex number field $\C$.

Then $S$ is absolutely convergent if and only if:

$\ds \sum_{n \mathop = 1}^\infty \cmod {a_n}$ is convergent

where $\cmod {a_n}$ denotes the complex modulus of $a_n$.