(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that

lim[itex]_{n \rightarrow ∞}[/itex] [itex]\frac{n! e^{n}}{n^{n+\frac{1}{2}}}[/itex] = [itex]\sqrt{2π}[/itex]

2. Relevant equations

3. The attempt at a solution

Alright so for this problem I noticed it looked kind of similar to the integral formula for a normal distribution from statistics with the 1/[itex]\sqrt{2π}[/itex] in it, but I'm not really sure what to do. I imagine there's a sine and cosine somewhere in there but I'm not exactly sure how to bring it in, maybe via taylor polynomials through the terms given?

I've yet no definitive solution but I've got some basic outlines of ideas.. I'm right now in Calc 2 so i expect there to be series and sequences involved..

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# Proving stirlings formula

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