Question

simplifique

n!/(n+1)!

(n+2)!/(n-1)!

(n+1)!+n!/ 2n



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Answer 1

$\frac{n!}{(n+1)!}=\frac{n!}{(n+1)n!}=\frac{1}{n+1}\\\\\\\frac{(n+2)!}{(n-1)!}=\frac{(n+2)n(n-1)!}{(n-1)!}=n(n+2)\\\\\\\frac{(n+1)!+n!}{2n}=\frac{(n+1)n(n-1)!+n(n-1)!}{2n}=\frac{n((n+1)(n-1)!+(n-1)!}{2n}=\frac{(n-1)!(n+2)}{2}$