Question

Análise Combinatória Fatorial​

Answer 1

$a)\ \dfrac{n!}{(n-1)!}\\ \\\dfrac{n(n-1)!}{(n-1)!}\\ \\\boxed{= n}\\\\b) \dfrac{(n+4)!}{(n+2)!+(n+3)!} \\\\\\\dfrac{(n+4)(n+3)(n+2)!}{(n+2)!+(n+3)(n+2)!}\\\\\\\dfrac{(n+4)(n+3)(n+2)!}{(n+2)!([1 + (n+3)]}\\\\\\\dfrac{(n+4)(n+3)}{(n+4)}\\\\\boxed{= (n+3)}\\\\\\c) \dfrac{(n-1)! + n!}{(n+1)!} \\\\\\\dfrac{(n-1)! + n(n-1)!}{(n+1)n(n-1)!}\\\\\dfrac{(n-1)! (1 + n)}{(n+1)n(n-1)!}\\\\\\\dfrac{(n+1)}{(n+1)n}\\ \\\boxed{= \dfrac{1}{n}}$

Abraços!