Question

determinati n apartine n* pentru care (n+1)!/(n-1)!=56

Answer 1

(n + 1)! = 1 * 2 * 3 * ... (n-1) * n * (n+1)

(n - 1)! = 1 * 2 * 3 * ... * (n-1)

Atunci:

(n+1)!/(n-1)! = n * (n+1)

n(n+1) = 56

n^2 + n - 56 = 0

Delta = b^2 - 4ac = 1 - 4*1*(-56) = 1 + 224 = 225

Radical delta = radical 225 = 15

n1 = (-b + radical delta)/2a = (-1+15)/2 = 14/2 = 7, solutie corecta, deoarece apartine multimii N*

n2 = (-b - radical delta)/2a = (-1-15)/2 = -16/2 = -8, solutie care nu corespunde conditiei, deoarece nu apartine N*

R: n = 7