Question

(n+2)!*(n-1)!/(n+1)!*n!=6/5

Answer 1

Olá, Ravelaf.

$\frac{(n+2)!\cdot(n-1)!}{(n+1)!\cdot n!}=\\\\ =\frac{(n+2)(n+1)n(n-1)!\cdot(n-1)!}{(n+1)n(n-1)!\cdot n(n-1)!}=\\\\ =\frac{(n+2)(n+1)n(n-1)!(n-1)!}{n(n+1)n(n-1)!(n-1)!}=\\\\ =\frac{n+2}{n}=\frac65\Rightarrow\\\\5n+10=6n\Rightarrow\\\\ 6n-5n=10\Rightarrow\\\\ \boxed{n=10}$