Is the series Convergent?

$$\sum\_{n=1}^{\infty} \ \left(1 + \frac{1}{n}\right)^{-n}$$

My attempt would be to use the binomial theorem and since the same series raised to n converges to e, then this series converges to 

$$\frac{1}{e}$$

Is the series Absolutely Convergent?

$$\sum\_{n=1}^{\infty} \ (-1)^n\frac{1}{2^n}\left(4-\frac{1}{n}\right)$$

A part of me says it converges absolutely since the limit of the absolute value of the expression is zero.

Appreciate any guidance