Question

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

Answer 1

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

 

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

Answer 2

$1) frac{n!}{(n+2)!} = frac{n!}{n!*(n+1)*(n+2)} = frac{1}{(n+1)(n+2)}=frac{1}{n^2+3n+2}$

 

$2) frac{(n+1)!}{(n-2)!}= frac{(n-2)!*(n-1)*n*(n+1)}{(n-2)!}=(n-1)*n*(n+1)=n^3-n$