Wednesday, December 9, 2015

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.

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