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!?
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.