Question

Simplifique ou resolva essa equação fatorial
$\frac{(n - 1)}{(n + 1) - n} = \frac{1}{81}$
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Answer 1

Resposta:

Explicação passo-a-passo:

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

obs o valor n= -9 não nos interessa