# Thread: Absolute convergence of complex series

1. ## Absolute convergence of complex series

Am I right in thinking a series converges absolutely if the modulus of the sum converges?

I have a question with two summations,

[Sum from n=1 to inf] ( i^n ) / n

[Sum from n=1 to inf] ( i^n ) / n^2

Asking which of these (if any) converge absolutely, with reasoning.

Intuitively they both converge absolutely, but the second one faster as the divisor would become greater quicker?

$\sum_{i=1}^n \frac 1 n$
$\frac 1 1 + \frac 1 2 + \frac 1 3 + \frac 1 4 +$