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Also elementary, but here is a proof that $C_n = \binom{2n}{n} - \binom{2n}{n+1} = \frac{\binom{2n}{n}}{n+1},$ where $C_n$ is the $n$th Catalan number. http://utdallas.edu/~hagge/images/Catalan.pdf Sorry for the link; new users may not use image tags. Here's the image:
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Also elementary, but here is a proof that $C_n = \binom{2n}{n} - \binom{2n}{n+1} = \frac{\binom{2n}{n}}{n+1},$ where $C_n$ is the $n$th Catalan number. http://utdallas.edu/~hagge/images/Catalan.pdf Sorry for the link; new users may not use image tags. |
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