calculus - How to find $lim_{nto infty}{frac{n^{n-1}}{n!}}$

What method should I use for this limit?

$$\lim_{n\to \infty}{\frac{n^{n-1}}{n!}}$$

I tried ratio test but I ended with the ugly answer

$$\lim_{n\to \infty}\frac{(n+1)^{n-1}}{n^{n-1}}$$
which would go to 1? Which means we cannot use ratio test. I do not know how else I could find this limit.