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I would like to see some detailed solution for $$\frac{n!}{\sqrt{2\pi n} \left(\frac{n}{e}\right)^n}$$ as $n\to\infty$. I know that the answer is 1 but i am not sure why? Here is what is tried:

I rewrote the stirling's formula like this. $$\frac{(e/n)\cdot (2e/n)\cdot (3e/n)\cdots (ne/n)}{\sqrt{2\pi n}}\to 0$$ as $n\to \infty$. I am not sure where I went wrong.


marked as duplicate by Antonio Vargas, Community Jan 26 '16 at 22:18

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  • $\begingroup$ Can you please explain what was wrong in re writing the form? $\endgroup$ – Ruthvik Vaila Jan 26 '16 at 20:29
  • 1
    $\begingroup$ How do conclude that $\frac{(e/n)\cdot (2e/n)\cdot (3e/n)\cdots (ne/n)}{\sqrt{2\pi n}}\to 0$? $\endgroup$ – leonbloy Jan 26 '16 at 21:43

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