let $\sum_{n=1}^\infty a_n \ \ a_i > 0 $ be convergent then prove that $\sum_{n=1}^\infty a_n^{\frac{n}{n+1}}$ is convergent.

Question

Let $\sum_{n=1}^\infty a_n \ , \ a_i > 0 $ be convergent.

I need to prove that $$\sum_{n=1}^\infty a_n^{\frac{n}{n+1}}$$ is convergent.

How should I prove it? Where should I start?