Consider the series

where

Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.

The series converges absolutely.

*Proof.* For each positive integer the term appears at most twice (appearing twice in the case that is a perfect square), and no other terms are in the series. Hence, we apply the comparison test,

Since this last series converges, we conclude that the converges by the comparison test