I have some reasons to believe that this equation is true:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\lim_{n\to\infty} \frac{\sqrt{n}}{2^{2n}} \frac{(2n)!}{(n!)^2} = \frac{1}{\sqrt{\pi}}

[/tex]

Anyone having idea of the proof? I don't even know how to prove that the limit is strictly between zero and infinity.

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# Difficult limit formula

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