For a sequence of non negative numbers, if the series converges, then the series of the sequence raised to p also converges if p>=1

Let $p \geqslant 1$ and let $(a_n)$ be a sequence of non-negative numbers. Then if $\sum\limits_{n=1}^\infty a_n$ converges, so does $\sum\limits_{n=1}^\infty a_n^p$. Prove this statement.

Sorry, we have just started learning series in class, but I have this homework problem and can't get anywhere. Any help/hints appreciated!

Eventually, $a_n<1$, then $a_n^p<a_n$ so...?