Question

simplifique:

(n+1)!+n!/(n+2)! (n pertencente aos Naturais)

Answer 1

Sabe-se que n! = n×(n-1)×(n-2)×...×2×1. Então,

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

Answer 2

Resposta:

Explicação passo-a-passo:

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