Question

Fatorial
(n + 1)! = 9n!

Answer 1

$(n+1)!=9n!\\ \\ \frac{(n+1)!}{n!}=9\\ \\\frac{(n+1)\not{n!}}{\not{n!}}=9\\ \\n+1=9\\ \\\boxed{\therefore~n=8}$

Answer 2

$(n+1)!=9n!$

Observe que, $(n+1)!=(n+1)n!$.

Assim, $(n+1)n!=9n!$

$\dfrac{(n+1)n!}{n!}=\dfrac{9n!}{n!}$

$(n+1)=9~~\Rightarrow~~\boxed{n=8}$

De fato, pois $(8+1)!=9\cdot8!$