- #1

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[tex]

\begin{pmatrix} 2(m+1) \\ k \end{pmatrix} = \frac{(2m)!}{k!(2m - k)!} \cdot \frac{(2m+2)(2m+1)}{(2m+2-k)(2m+1-k)}

[/tex]

The inductive hypothesis is to assume the thing on the left is biggest for [itex]k = m[/itex], but the second fraction gets bigger as you make [itex]k[/itex] bigger. So...what to do! Any comments? Thanks!