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.

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