Converges of sin functions with fractions $$\sum \frac{\sin(n)}{n^{3/2}}$$
What strategy would I use to test for convergence for this series?

Notice 
$$ | \sin \alpha | \leq 1 $$
for all $\alpha$. Hence
$$ a_n = \frac{\sin (n) }{n^{3/2}} \leq \frac{1}{n^{3/2} } = b_n$$
Obviously, $\sum b_n$ converges. Now, by comparison test, $\sum a_n$ must converge.
