Question

Se (n! + (n - 1)!)/((n + 1)! - n!) = 6/25 então n=?​

Answer 1

Explicação passo-a-passo:

n! + ( n-1)! 6

________= ___

(n+1)! - n! 25

n . (n-1)! + ( n-1)! 6

_______________ = ___

(n+1).n.(n-1)! - n.(n-1)! 25

(n-1)! . [ n + 1] 6

______________ = ____

(n-1)! . [ (n+1).n - n] 25

n + 1 6

______________= ______

n² + n - n 25

n+1 6

_______= ___

n² 25

6n² = 25 (n+1)

6n² = 25 n +25

6n² - 25n - 25=0

∆= (-25)² -4.6.(-25)

∆= 625 + 600

∆= 1225

n= - (-25) + √1225/2.6

n= 25 + 35/12

n= 60/12

n= 5