Qual é o valor de n?
[tex]\Large\displaystyle\text{$\begin{gathered}\sf{\frac{(n+2)!-n!}{5!}=330}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\sf{\frac{(n+2)!-n!}{5!}=330}\end{gathered}$}[/tex]
More Questions From This User See All
Lista de comentários
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[tex]\Delta=3\²-4.1.(-54)\\\\\Delta = 9 + 216\\\\\Delta=225\\\\n=\frac{-3\pm15}{2} \\\\n=-9~(nao~serve)[/tex]