જો ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .... + {C_n}{x^n}$, તો ${C_0}{C_2} + {C_1}{C_3} + {C_2}{C_4} + {C_{n - 2}}{C_n}$= . . .

  • A

    $\frac{{(2n)!}}{{(n + 1)!(n + 2)!}}$

  • B

    $\frac{{(2n)!}}{{(n - 2)!(n + 2)!}}$

  • C

    $\frac{{(2n)!}}{{(n)!(n + 2)!}}$

  • D

    $\frac{{(2n)!}}{{(n - 1)!(n + 2)!}}$

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$\left( {\begin{array}{*{20}{c}}{20}\\0\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\1\end{array}} \right)$$+$$\left( {\begin{array}{*{20}{c}}{20}\\2\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\3\end{array}} \right)$$+…..-……+$$\left( {\begin{array}{*{20}{c}}{20}\\{10}\end{array}} \right)$ નો સરવાળો. 

  • [AIEEE 2007]

$\sum\limits_{k = 0}^{10} {^{20}{C_k} = } $