Question

O valor de n na expressão abaixo e:
(n-1)! =1/81
(n+1)!-n!

Answer 1

Resposta:

n = 9

Explicação passo-a-passo:

$\frac{(n-1)!}{(n+1)!-n!} = \frac{1}{81} \\\\\frac{(n-1)!}{(n+1)n(n-1)!!-n(n-1)!} = \frac{1}{81}\\\\\frac{(n-1)!}{(n-1)![(n+1)n-n]} = \frac{1}{81}\\\\\frac{1}{(n+1)n-n} = \frac{1}{81}\\\\n^{2} + n - n = 81\\\\n^{2} = 81\\\\n = 9$