Show that if the partial sums of $s_n$ of the series $\sum_{k=1}^{\infty} a_k$ satisfy |$s_n$| $\leq Mn^r$ for some $r < 1$

Then the series $\sum_{n=1}^{\infty} \frac{a_n}{n}$ converges.

I really wanted to apply dirichlet's test here, but I cant seem to find a bound for $s_n$.

Any help or insight is deeply appreciated.


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