- #1

Potatochip911

- 318

- 3

## Homework Statement

Evaluate the limit ##\lim_{n\to\infty} \dfrac{n^n}{n!}##

## Homework Equations

Ratio test: ##a_{n+1}*\dfrac{1}{a_n}##

## The Attempt at a Solution

I was having trouble evaluating this so I tried to use the ratio test which unfortunately leads to ##\lim_{n\to\infty} \dfrac{n}{n+1}## which just ends up being 1 which does not tell me whether the series is convergent or divergent. Alternatively I tried looking at it like this but I couldn't see where to go from there $$\lim_{n\to\infty} \frac{n}{1} \frac {n}{2} \frac {n}{3} \cdots \frac{n}{n} $$