How to determine if the series $\sum^\infty_{n=1} \frac{1}{3+\cos(2^n)} $ converges or diverges?

Question

$\sum^\infty_{n=1} \frac{1}{3+\cos(2^n)} $

I know that $2\le 3+\cos(2^n)\le4 \Rightarrow \frac{1}{4}\le\frac{1}{3+\cos(2^n)} \le1/2 \Rightarrow \frac{1}{3+\cos(2^n)} \ge \frac{1}{4}$. Which test can I use to determine whether the series converges or not?