If 2 / 1 + 6 / 1 + 12 / 1 ········ n + (n + 1) / 1 equals 2006 / 2005, then n equals?

Original formula = 1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 +. + 1 / n-1 / (n + 1)
=1-1/n
=(n-1)/n
=2005/2006
n=2006