Assume that $\sum_{n}^{\infty} a_n$ is a non-negative, convergent series. Let $f$ be a continuous function with domain $\mathbb{R}$. I have to figure out if the series
$\sum_{n}^{\infty} a_n f(\sin n)$
- converge
- diverge
- not enough information to decide
The only possible test that is applicable here is I think basic comparison test, somehow using the fact that sin is bounded, but I have no idea how to proceed. Could anyone help me out?