Question

Simplifique:
a) n! / (n-1)
b) (n+2)! / (n+3)!
c) (n+4)! / (n+2)! + (n+3)!
d) (n-1)! - n! / (n+1)!

*Preciso que faça a resolução. Quem puder me ajudar, eu agradeço!!​

Answer 1

Resposta:

Explicação passo-a-passo:

a)

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

b)

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

c)

$\frac{(n+4)!}{(n+2)!+(n+3)!}=\frac{(n+4)(n+3)(n+2)!}{(n+2)!+(n+3)(n+2)!}=\frac{(n+4)(n+3)(n+2)!}{(n+2)![1+n+3]}=\frac{(n+4)(n+3)}{[n+4]}=n+3$

d)

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