Question

resolva a equacao (n+2)! + (n+1)! = 15*n!

Answer 1

$\displaystyle i)~~~~(n+2)!+(n+1)!=15n!\\\\ii)~~~(n+2)(n+1)n!+(n+1)n!=15n!\\\\iii)~~n![(n+2)(n+1)+(n+1)]=15n!\\\\iv)~~~n!(n+1)[(n+2)+1]=15n!\\\\v)~~~~\frac{n!(n+1)[(n+2)+1]}{n!}=15\\\\vi)~~(n+1)(n+2)+n+1=15\\\\vii)~~n^2+4n-12=0\\\\\\viii)~~N=\frac{-4\pm\sqrt{4^2+4\cdot 12}}{2}=\begin{cases}n'=\frac{-4+8}{2}=2\\n''=\frac{-4-8}{2}=-6\end{cases}$

ou seja:
$S=\{-6,2\}$
(solução)

Caso haja dúvidas, comente abaixo e se houver problemas para visualizar a resposta, acesse-a através do link https://brainly.com.br/tarefa/10214896
Bons estudos!