Divergent Series/Examples/n over n^2 + i

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

is divergent.

Proof
Then we have:

From Harmonic Series is Divergent, $\displaystyle \sum_{n \mathop = 1}^\infty \dfrac 1 n$ is a divergent series.

The result follows from Convergence of Series of Complex Numbers by Real and Imaginary Part.