Sum of series involving 1+cos(n)... $$\sum_{n=2}^\infty{1+\cos(n)\over n^2}$$ 
I justified that it converges absolutely by putting it less than to $\frac{1}{n^2}$ where $p=2>1$ meaning that it converges absolutely. Would this be a correct way to solve this problem? 

Yes, as you say, $$\sum_{k=2}^\infty\left \lvert \frac{1+\cos(n)}{n^2}\right \lvert\leq \sum_{k=2}^\infty \frac{2}{n^2}=\frac{\pi^2}{3}-2,$$
which shows absolute convergence.
