I know that $\frac{n!}{(n+1)!}$ can be reduced to $\frac{1}{n+1}$, but i'm not sure about this one.
$$\sum_{n=1}^\infty \frac{(-1)^nn!}{(n+100)!}$$
In my notes, my professor reduced it to a p-series such as $\frac{1}{n^{100}}$, but I'm not able to replicate his method. How would I go about reducing this series to determine its convergence?