Are the following series convergent? If yes, where will they converge?
$$\sum_{n=1}^\infty{\frac{\sin{e^n}} {n}}$$
$$\sum_{n=1}^\infty\left({\frac{\sin{e^n}} {n}}\right)^2$$
$$\sum_{n=1}^\infty{\frac{\arctan{e^n}} {n}}$$
$$\sum_{n=1}^\infty{\frac{\cos{e^n}} {n}}$$