# Thread: Help classifying a series

1. ## Help classifying a series

I need to classify the following series:

$\sum_{n=n_0}^\infty\sqrt{a_n}$

with $(a_n)\ge0$ and $\sum_{n=n_0}^\infty a_n$ $\mathbb{C}$

I guess the question on the whole is whether i can classify any of the following series:

$\sum_{n=n_0}^\infty (a_n)^r$ , $\forall r\in\mathbb{Z}$

based on $\sum_{n=n_0}^\infty a_n$ being convergent

As far as I can tell (using the Comparison Test), $\sum_{n=n_0}^\infty (a_n)^r$ will converge if $r > 1$, but what if $r < 1$?