Convergent sum involving the divisor function Here's a doosy posed as a challenge question;
Let $d(n)$ be the number of divisors of $n$. Prove that $d(n)$ is a multiplicative function of $n$ and show that for any natural number $r \ge 1$, the series 
$$\sum_{n=1}^{\infty}{\frac{d(n)^r}{n^s}}$$
converges absolutely for $s \gt 1$. Deduce that for any $\epsilon \gt 0, d(n) = O(n^{\epsilon}).$
I'm completely stuck. When I see $O$ terms, I automatically think partial summation, but I don't see that working here. Not sure how to approach this, any help is appreciated

Your series is related to the Dirichlet series.
