Answer
The series is absolutely convergent.
Work Step by Step
$\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{(n+1)^{100}100^{n+1}}{(n+1)!}}{\frac{n^{100}100^{n}}{(n)!}}|$
$=\lim\limits_{n \to \infty}(\frac{n+1}{n})^{100}\frac{100}{n+1}$
$=0 \lt 1$
The series is absolutely convergent.