Question

Calcule o valor de X na expressão (x + 1)! / x! = 5 (Análise Combinatória)

Answer 1

$\frac{(x + 1)!}{x!}$ = 5
$\frac{(x + 1)(x)!}{x!}$ = 5
x + 1 = 5
x = 5 - 1
x = 4

Answer 2

$\displaystyle \mathsf{\frac{(x + 1)!}{x!} = 5}\\ \\ \displaystyle \mathsf{\frac{(x + 1).x!}{x!} = 5}\\ \\ \displaystyle \mathsf{x + 1 = 5}\\ \displaystyle \mathsf{x = 5 - 1}\\ \displaystyle \boxed{\mathsf{x = 4}}$

Resposta: x = 4