Question

simplifique

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

Answer 1

Olá Amanda.



Organizando e simplificando a fração:

$\mathsf{\dfrac{(n+1)!}{(n-2)!}}\\\\\\\mathsf{\dfrac{(n+1)\cdot n\cdot (n-1)\cdot (n-2)!}{(n-2)!}}\\\\\\\boxed{\mathsf{(n+1)\cdot n\cdot(n-1)}}\\\\\\\mathsf{ou}\\\\\\\mathsf{(n+1)\cdot(n-1)\cdot n}\\\\\mathsf{(n^2-1)\cdot n}\\\\\boxed{\mathsf{n^3-n}}$


Dúvidas? comente.

Answer 2

Lembre que: (n+1)! pode ser escrito como  (n+1).n.(n-1)(n-2)!

Substituindo na fração, temos:

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