Prove that(series)...?

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May 3rd 2009, 11:34 PM
fardeen_gen

Prove that(series)...?

Let $n\in\mathbb{N}$ . Prove that:
$\sum_{k = 0}^{m}\frac{{2n - k\choose k}}{{2n - k\choose n}}\cdot \frac{2n - 4k + 1}{2n - 2k + 1}\cdot 2^{n - 2k} = \frac{{n\choose m}}{{2n - 2m\choose n - m}}\cdot 2^{n - 2m}$

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