# Math Help - Find an example of a sequence

1. ## Find an example of a sequence

Find an example of a non-negative sequence $\{a_n\}$ such that $\textstyle \sum a_n^2$ converges but $\textstyle \sum \frac {a_n} n$ diverges.

I only know what it cannot be. It cannot be $\frac 1 {n^s}$ for any real s, it cannot be $\frac 1 {log^s n}$ for any real s, and obviously any geometric series won't work...

I'm stuck. I would appreciate a hint.

2. ## Re: Find an example of a sequence

Scratch that... I thought it was possible, but I think I just proved that such a sequence is impossible.