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 (Wayback Machine)
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Here's the image:
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:
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 (Wayback Machine)
Sorry for the link; new users may not use image tags.
Here's the image:
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:
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.
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:
