Thread: Stirling's approximation

Hi, I was just checking out the proof of this in William Feller's book, and it jumps from the arithmetic mean of (nlog(n)-n) and ((n+1)log(n+1)-n) to ((n+(1/2))log(n)-n). I'm not seeing it. The book is certainly a good read, but nonetheless I'm missing out. Any hints?

Prove that


Hint: Divide numerator and denominator by .

Alright.
It's not equal, it's only an approximation of the approximation.
And this is where the ~ comes from then?

Originally Posted by eulcer

And this is where the ~ comes from then?

Right.