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**zhengcl86** Latex is pretty sweet! just learned how to use this, so for this question

Prove the following combinatorial identity if $\displaystyle {1}\leq k<n$. This identity is known as the hexagon identity and relates terms in Pascal's Triangle.

$\displaystyle \left(\begin{array}{cc}n-1\\k-1\end{array}\right)$ $\displaystyle \left(\begin{array}{cc}n\\k+1\end{array}\right)$ $\displaystyle \left(\begin{array}{cc}n+1\\k\end{array}\right)$ = $\displaystyle \left(\begin{array}{cc}n-1\\k\end{array}\right)$ $\displaystyle \left(\begin{array}{cc}n\\k-1\end{array}\right)$ $\displaystyle \left(\begin{array}{cc}n+1\\k+1\end{array}\right)$

where do i even begin to solve this? The Pascal's Triangle i kind of understand but the rest is news to me.