Does $\sum_{n=1}^\infty \frac{1}{\log(e^{n}+e^{-n})}$ converge or diverge? How would I show that the following series converges or diverges?
$$\sum_{n=1}^\infty  \frac{1}{\log(e^{n}+e^{-n})}$$
Any help would be appreciated.

HINT:
$$\log(e^n+e^{-n})=n+\log(1+e^{-2n})\le n+e^{-2n}\le 2n$$
