Answer
Converges Absolutely
Work Step by Step
Consider $a_n=\dfrac{n+1}{n!}$
By the Ratio Test:
$l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_n}|=\lim\limits_{n \to \infty} |\dfrac{\dfrac{(n+1)+1}{(n+1)!}}{\dfrac{n+1}{n!}}|$
or, $=\lim\limits_{n \to \infty} |\dfrac{\dfrac{n+2}{n!(n+1)!}}{\dfrac{n+1}{n!}}|$
or, $\lim\limits_{n \to \infty} \dfrac{(n+2)}{(n+1)^2}=\lim\limits_{n \to \infty} \dfrac{1}{(n+1)}+\lim\limits_{n \to \infty} \dfrac{1}{(n+1)^2}$
or, $\dfrac{1}{\infty}+\dfrac{1}{\infty}=0$
so, $l=0 \lt 1$
Thus, the series Converges Absolutely by the Ratio Test.
