Question

(Fatorial) Simplifique a expressão:

(n-1)! - n! / (n-1)!

Answer 1

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

Answer 2

n! = n.(n-1)!

Logo:

(n - 1)! - n.(n - 1)! / (n - 1)! =
= (n - 1)!.(1 - n) / (n - 1)! =
= 1 - n