Limit of series

1. Aug 20, 2008

ercagpince

1. The problem statement, all variables and given/known data
what is the limit of this expression?

$$lim_{n\rightarrow\infty}\frac{n^n}{n!}$$

2. Relevant equations

3. The attempt at a solution
I tried to make it look like $$\frac{x^n}{n!}$$ and also tried to apply the sandwich theorem, but got nothing logical.
Probably the limit is $$\infty$$, still I want to prove it mathematically.

2. Aug 20, 2008

Dick

You could take the log and use Stirling's approximation on the factorial.

3. Aug 20, 2008

ercagpince

Could you show it explicitly?

4. Aug 20, 2008

Dick

If you mean show the details, Isn't that your job? Did you look up Stirling's approximation? Or do you mean do it without Stirling's formula?

5. Aug 20, 2008

ercagpince

if you take the stirling's approximation there is no need to take log of the term on numerator.

6. Aug 20, 2008

Dick

Right, if you use the form n!~(n/e)^n. I was thinking of ln(n!)~n*ln(n)-n

7. Aug 20, 2008

ercagpince

thanks for the post