Question

Simplifique a expressão (n+1)!+n!/(n+2)! , (n e N , n maior ou igual 1

Answer 1

Explicação passo-a-passo:

$\dfrac{(n+1)!+n!}{(n+2)!} \geqslant 1 \\ \\ \dfrac{ \cancel{(n+1)!}+n!}{(n+2) \cancel{(n + 1)!}} \geqslant 1 \\ \\ \dfrac{n!}{(n+2)} \geqslant 1 \\ \\ n! \geqslant n + 2 \\ \\ \boxed{ \boxed{n \geqslant 3}}$