# Math Help - Very Hard Limit

1. ## Very Hard Limit

Verify numerically that:

limit as n->infinity of ((e^n)*(n!))/(n^(n+1/2))=sqrt(2*pi)

What do they mean by numerically? I know I could do L'H rule, but then how would I find the derivative of n!?

2. Originally Posted by twittytwitter
Verify numerically that:

limit as n->infinity of ((e^n)*(n!))/(n^(n+1/2))=sqrt(2*pi)

What do they mean by numerically? I know I could do L'H rule, but then how would I find the derivative of n!?
You're probably expected to substitute larger and larger values of n and note the sequence of resulting values ....

3. Ok thanks, so there's no algebraic way I could show this that is not too complicated?

4. Originally Posted by twittytwitter
Ok thanks, so there's no algebraic way I could show this that is not too complicated?
There is. But:

Originally Posted by twittytwitter
Verify numerically that:

limit as n->infinity of ((e^n)*(n!))/(n^(n+1/2))=sqrt(2*pi)

What do they mean by numerically? I know I could do L'H rule, but then how would I find the derivative of n!?
which means that an algebraic way is probably beyond your present capability.

5. Originally Posted by twittytwitter
Ok thanks, so there's no algebraic way I could show this that is not too complicated?
Check out Stirling's approximation - Wikipedia, the free encyclopedia

What you have is a somewhat inverted version of this approximation. There are many ways to show this, the two that I know involve approximating that Gamma integral for large argument.