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Show that $\log({n\choose n/2})=O(n)$,
I've tried to use stirling's formula but didn't get any close

Wolgwang
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convxy
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  • Can you show us how you used Stirling's formula? Even a weak version of it suffices to prove what you want... – jjagmath Nov 14 '20 at 15:12

1 Answers1

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Hint

$$\binom{n}{\frac{n}{2}}=\frac{n!}{\left(\frac{n}{2}!\right)^2}$$ $$\log \left(\binom{n}{\frac{n}{2}}\right)=\log(n!)-2\log \left(\frac{n}{2}!\right)$$

Use Stirling approximation twice and continue with Taylor expansion.

Claude Leibovici
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