Question

Sabendo que 8n! = ((x+2)! + (n+1)!)/n+1 o valor de n é



a) 2
b) 3
c) 4
d) 5
e) 6

Answer 1

Olá Jonathan.


Organizando e resolvendo a equação.


$\mathsf{8n!=\dfrac{(n+2)! + (n+1)!}{(n+1)}}\\\\\\\mathsf{8n!=\dfrac{(n+2)\cdot(n+1)\cdot n!+(n+1)\cdot n!}{(n+1)}}\\\\\\\mathsf{8\diagup\!\!\!\!n!=\dfrac{(n+1)\cdot\diagup\!\!\!\!n!\cdot(n+2+1)}{(n+1)}}\\\\\\\mathsf{8=n+3}\\\\\mathsf{8-3=n}\\\\\boxed{\mathsf{n=5}}$

Dúvidas? comente.