# Rate of convergence in the Stirling formula [closed]

By the Stirling formula, $$\lim \frac{\sqrt{2\pi n}\left(\frac{n}{e}\right)^n}{n!}=1.$$ How to estimate $$\left|\frac{\sqrt{2\pi n}\left(\frac{n}{e}\right)^n}{n!}-1\right|\quad ?$$

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Welcome to math.stackexchange. This should answer your question. –  Ragib Zaman Jun 26 '12 at 7:37
Very nice. Thanks a lot! –  deltuva Jun 26 '12 at 8:42