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# Simplify the following factorial:(2k+1)!/(2)(k!)?

Simplify the following factorial:(2k+1)!/(2)(k!)

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- SamwiseLv 71 decade agoFavorite Answer
(2k+1) * (2k) * (2k-1) * ... * (k+2) * (k+1) / 2

= (2k+1) * k * [(2k-1) * ... * (k+2) * (k+1)]

In the first step, I canceled out a factor of k! from the numerator and denominator.

In the second step, I canceled the 2 in the denominator with the 2 factor in the 2k, the only clearly even number in the numerator. I added the brackets to keep the ellipsis notation from becoming ambiguous. (Otherwise the k factor is out of sequence and makes that notation unclear.)

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