limits - Result of $lim_{ntoinfty} frac{{x}^{100n}}{n!}$

The task is to $\lim_{n\to\infty} \frac{{x}^{100n}}{n!}$. n is an integer. I've tried to use Stolz theorem, but that doesn't seem to give any result.

Thank you for your help.

Answer

By ratio test

$$\frac{{x}^{100(n+1)}}{(n+1)!}\frac{n!}{{x}^{100n}}=\frac{x^{100}}{n+1}\to 0$$

then

$$\lim_{n\to\infty} \frac{{x}^{100n}}{n!}=0$$