Use comparison test to find if the series $\frac{\sin n \cos n}{15^n}$ diverges/converges $$\sum_{n=1}^{\infty} \frac{\sin n \cos n}{15^n}$$
Since it's a problem that involves trigonometric functions do we use the $A_n$ and $B_n$? Or is there a different approach? 

We show that 
$$\sum_1^\infty \left|\frac{\sin n\cos n}{15^n}\right|\tag{1}$$
converges. That means that the series we were given converges absolutely, and hence converges. 
Note that $|\sin n\cos n|\le 1$. It follows that
$$\left|\frac{\sin n\cos n}{15^n}\right|\le \frac{1}{15^n}.$$
The series $\sum_1^\infty \frac{1}{15^n}$ is a convergent geometric series. So by Comparison, the series (1) converges, and therefore our series does. 
