I'm having trouble with 3 series questions involving trig.

1. $\displaystyle \sum_{n=1}^\infty \frac{cos^2 (n)}{n^2 +1}\$

2. $\displaystyle \sum_{n=0}^\infty \frac{1+ sin (n)}{10^n}\$

3. $\displaystyle \sum_{n=1}^\infty \frac{arctan (n)}{n^{1.2}}\$

For the most part I know that they are convergent, but I am unable to show it. I have attempted to demonstrate it using a limit comparison test, but have so far been unsuccessful.