Question

Simplifique a expressão
(n-1)! / (n+2)!


(n-2)!/n!

(n+3)!/(n+1)!

Answer 1

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

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

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

Answer 2

Resposta:

Explicação passo-a-passo:

Gosto de resolver questões digitadas corretamente.

$a)\frac{(n-1)!}{(n+2)!}=\frac{(n-1)!}{(n+2)(n+1)n(n-1)!}=\frac{1}{n(n+1)(n+2)}\\\\b)\frac{(n-2)!}{n!}=\frac{(n-2)!}{n(n-1)(n-2)!}=\frac{1}{n(n-1)}\\\\c)\frac{(n+3)!}{(n+1)!}=\frac{(n+3)!}{(n+1)!}=\frac{(n+3)(n+2)n+1)!}{(n+1)!}=(n+3)(n+2)$