Question

Simplifique as expressões :
a) (n+3)! . (n-2)! /  n! . (n-1) !
 
b) (n-2)! / (n-3) + (n+1)! / (n-2)!

Answer 1

a)

$\frac{(n+3)!(n-2)!}{n!(n-1)!}=\frac{(n+3)(n+2)(n+1)n!(n-2)!}{n!(n-1)(n-2)!}=\frac{(n+3)(n+2)(n+1)}{n-1}=\\ \\ \frac{n^3+6 n^2+11 n+6}{n-1}$

b)

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