Question

Simplifique a expressão:

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

Answer 1

Oi Estter.

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