№1717
\[\begin{array}{l}
{\text{Докажите тождество:}} \hfill \\
\sum\limits_{k = 0}^n {\frac{{\left( {2n} \right)!}}{{{{\left( {k!} \right)}^2}{{\left( {\left( {n - k} \right)!} \right)}^2}}}} = {\left( {C_{2n}^n} \right)^2}. \hfill \\
\end{array}\]
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