Prove that (2n)! / n! is equivalent to...?

Prove that (2n)! / n! = 2^n(1x3x5...(2n-1)).

Please show the complete steps. Explain, if necessary. Thanks!!

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  • z
    Lv 5
    9 years ago
    Favourite answer

    (2n)!

    = 1x2x3x4x...x(2n-1)x(2n)

    = [1x3x5x...x(2n-1)] x [2x4x6x8x...x(2n]

    = [1x3x5x...x(2n-1)] x [1x2x3x4x...x(n) * 2x2x2x...x2]

    = [1x3x5x...x(2n-1)] x n! x 2^n

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