Hi, im having a little trouble with this proof:(adsbygoogle = window.adsbygoogle || []).push({});

Let n be a positive integer. What is the largest binomial coefficient [tex]C(n,r)[/tex] where r is a nonnegative integer less than or equal to n? Prove your answer is correct.

So let [tex]r = \lfloor{\frac{n}{2}\rfloor} [/tex] or [tex]r = \lceil{\frac{n}{2}\rceil} [/tex] then [tex]\left( \begin{array}{c} n \\ r \end{array} \right)[/tex] is the largest binomial coefficient.

Now im having trouble with the proof. Where do i begin?

Maybe something like this?

[tex]\left( \begin{array}{c} n \\ \lfloor \frac{n}{2} \rfloor \end{array} \right) = \frac{n!}{\left(\lfloor \frac{n}{2} \rfloor \right)! \left(n - \lfloor \frac{n}{2} \rfloor \right)!} = ......[/tex]

Am i on the right track?

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# A proof.

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