calculus - Prove or disprove that the series is converge

I need to prove or disprove the following statement -

If $a_{n} >= 0 , p > 1$ , and $\sum_{i=1}^\infty{a_{n}}$ converge , then $\sum_{i=1}^\infty{a_{n}^p}$ converge

Well , It looks like a wrong statement but I couldn't think about familiar counterexample.
I would like to get a hint.

Thanks!