Question

Simplifique e calcule o valor de n: (Fatorial)
(n-1)! / (n+1)!-n! = 1/81

Answer 1

Olá!

$\frac{(n-1)!}{(n+1)!-n!}=\frac{1}{81}$
$\frac{(n-1)!}{(n+1)n!-n!}=\frac{1}{81}$
$\frac{(n-1)!}{n!((n+1)-1)}=\frac{1}{81}$
$\frac{(n-1)!}{n!(n)}=\frac{1}{81}$
$\frac{(n-1)!}{(n-1)!(n^2)}=\frac{1}{81}$
$\frac{1}{(n^2)}=\frac{1}{81}$
$n^2=81$
$n=\sqrt{81}$

$n=9$