Divergent Series/Examples/((2+3i) over (3-2i))^n

Example of Divergent Series
The complex series defined as:
 * $\ds S = \sum_{n \mathop = 1}^\infty \paren {\dfrac {2 + 3 i} {3 - 2 i} }^n$

is divergent.

Proof
Thus the sequence $\sequence {\paren {\dfrac {2 + 3 i} {3 - 2 i} }^n}$ does not tend to zero.

Hence from Terms in Convergent Series Converge to Zero it follows that $S$ is divergent.