Absolutely Convergent Complex Series/Examples

Examples of Absolutely Convergent Complex Series

Example: $\paren {\dfrac z {1 - z} }^n$

The complex series defined as:

$\ds S = \sum_{n \mathop = 1}^\infty \paren {\dfrac z {1 - z} }^n$

is absolutely convergent, provided $\Re \paren z < \dfrac 1 2$.