Question

Calcule o valor de n em: (n+3)! / (n+1) - (n+2)! / n! = 20

Answer 1

(n + 3)! / (n + 1)! - (n + 2)! / n! = 20

(n + 3)(n + 2)(n + 1)!/(n + 1)! - (n + 2)(n + 1)n!/n! =20

(n + 3)(n + 2) - (n + 2)(n + 1) = 20

pondo em evidencia (n + 2)

(n + 2)(n + 3 - (n + 1)) = 20

(n + 2)(n + 3 - n - 1) = 20

(n + 2).2 = 20

2n + 4 = 20

2n = 20 - 4

2n = 16

n = 16/2

n = 8

R.: n = 8