Problem

Determine whether each of the following series converges. Justify your answers.

(a) (5 pts) $\displaystyle \sum_{n=1}^{\infty}\left(1+\frac{1}{n}\right)^n$.

(b) (5 pts) $\displaystyle \sum_{n=1}^{\infty}\frac{\sin(n+1)}{n^2}$.

(c) (5 pts) $\displaystyle \sum_{n=1}^{\infty}\frac{\ln(n)}{n^{1.2}}$.

(d) (5 pts) $\displaystyle \sum_{n=1}^{\infty}\frac{(n!)^2}{(2n)!}$.