Question

Qual é o valor de n?

$\Large\displaystyle\text{ \begin{gathered}\sf{\frac{(n+2)!-n!}{5!}=330}\end{gathered} }$​

Answer 1

Resposta:

(n + 2)! - n! = 2.3.5.11.5!

(n +2)(n + 1) n! - n! = 6.5! 5.11

n![(n + 2)(n + 1) - 1] = 6! . 55

n!(n² + 3n + 2 - 1) = 6! . 55

n!(n² + 3n + 1) = 6! . 55

n! = 6

n! = 3!

n = 3 (não serve)

ou

n² + 3n + 1 = 55

n² + 3n - 54 = 0

n = 6$\Delta=3\²-4.1.(-54)\\\\\Delta = 9 + 216\\\\\Delta=225\\\\n=\frac{-3\pm15}{2} \\\\n=-9~(nao~serve)$