Find upper and lower bounds for n/m

[mathvision]

If n>m>1, find upper and lower bounds for n!/m!

Answer: upper bound = {[(n+1)^(n+1)]/[(m+1)^(m+1)]}*e^(-(n-m))
lower bound = [(n^n)/(m^m)]*e^(-(n-m))

This is from a chapter on finding bounds for sum of series. Can someone please explain how to arrive at the answer? Thanks!

 

[uart]

Hi mathvision. It looks like they are probably using Stirling's approximation to derive those bounds. http://en.wikipedia.org/wiki/Stirling's_approximation