prove that 2nCn= (2n x [1x3x5x.......2n-1])/n!.

2n Cn = 2n!(2n - n)! n!=(2n)!(n!)2 = (2n) (2n - 1) (2n - 2)..........4.3.2.1(n!)2=[(2n)(2n - 2)(2n - 4)...4.2] [(2n-1) (2n-3).....3.1](n!)2=2nn(n-1)(n -2) ....2.11.3.5.......(2n-1)(2n-3)(n!)2=2nn!1.3.5.......(2n-1)(2n-3)(n!)2 = 2n1.3.5.......(2n-1)(2n-3)n!

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