Question

Resolva:

(n+2)!(n-1)!/n!(n+1)!

PRECISO URGENTEMENTE POR FAVOR!!!

Answer 1

Explicação passo-a-passo:

$\sf \dfrac{(n+2)!\cdot(n-1)!}{n!\cdot(n+1)!}$

Temos que:

• $\sf (n+2)!=(n+2)\cdot(n+1)!$

• $\sf n!=n\cdot(n-1)!$

Substituindo:

$\sf \dfrac{(n+2)!\cdot(n-1)!}{n!\cdot(n+1)!}$

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

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

$\sf =\red{\dfrac{n+2}{n}}$