Question

Simplifique a expressão fatorial e marque a resposta correta
(n + 2)! + (n + 1)! / (n + 1)!

a) n + 1
b) n + 2
c) n + 3
d) n + 4

Answer 1

$\boxed{\boxed{\boxed{\sf Alternativa \: C)n + 3}}}$

Para resolucionarmos a expressão fatorial, devemos expandi-lá usando n! = (n - 1)!.

$\sf \dfrac{ (n + 2)! + (n + 1)!}{(n + 1)!} \\ \\ \\ \sf \dfrac{(n + 2) \cdot(n + 1)! \: + (n + 1)!}{(n + 1)!}$

Agora iremos fatorar (x + 1)!, e simplificar (x + 1)!.

$\sf \dfrac{(n + 2 + 1) \: \cancel{\cdot(n + 1)!}}{ \cancel{(n + 1)!} } \\ \\ \\ \sf (n + 2 + 1) \\ \sf \boxed{\boxed{\boxed{\sf n + 3}}}$

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Att: Nerd1990

Answer 2

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

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

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

$n + 3$

$letra \: c)$