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$$\frac{ (2+x)!}{x!}$$ is there any formula for calculating this?

I think : x!(x+2)/x! then results in this true?

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$(2+x)! =(2+x) (1+x) x!$ – Claude Leibovici Feb 2 '14 at 10:24
up vote 2 down vote accepted

Assuming $x$ is a positive integer, then

$$ \frac{ (2+x)!}{x!} = \frac{(2+x)(1+x)x!}{x!} = (2+x)(1+x) = 2 + 3x + x^2$$

Notice by definition $n! = n \times (n-1) \times (n-2) \times ... \times 1 $

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