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