# Find the limit

1. Dec 29, 2004

### Ali 2

Hi ,

Evaluate the following limit :

$$\lim_{n\rightarrow\infty}\frac{n}{(n!)^{\frac1n}}=\lim_{n\rightarrow\infty}\frac{n}{\sqrt[n]{n!}}$$

Last edited: Dec 29, 2004
2. Dec 29, 2004

### NateTG

3. Dec 30, 2004

### Ali 2

I know about that .. the solution will be obtained easily by that method ..

but.. could you solve the question without stirling's approximation ?

Last edited: Dec 30, 2004
4. Dec 30, 2004

### dextercioby

I'm afraid Stirling's approximation provides the simplest approach.Keep in mind that u've to compute the limit of a sequence and u cannot make the transition to a function,due to a factorial in the denominator.Of course,that factorial can be put under the form
$$n!=\Gamma(n+1)$$
,but that won't do you any good,since it still involves discrete values for "n".

Daniel.