Evaluate Limit with Factorials: \lim_{n \to \infty}

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SUMMARY

The limit evaluation discussed is \lim_{n \to \infty} \frac{n!}{\left(\frac{n+p}{2}\right)!\left(\frac{n-p}{2}\right)!}2^{-n}. Using Stirling's approximation, which states that n! \sim \sqrt{2 \pi n} \left(\frac{n}{e}\right)^n, the limit approaches zero as n approaches infinity. This conclusion is supported by the growth rates of the factorial terms in the numerator and denominator, confirming that the limit indeed converges to zero.

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pseudogenius
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Anyone know of any method to evaluate this limit,

[tex]\lim_{n \to \infty} \frac{n!}{\left(\frac{n+p}{2}\right)!\left(\frac{n-p}{2}\right)!}2^{-n}[/tex]

it seems to go to zero, but I have no way to be sure.
 
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What did you get from Stirling's approximation?
 

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