1 / 2 + 1 / 6 + 1 / 12 +. = n times N + 1 = 2006 / 2005, n = how much

2005/2006=1/（2*1）+1/（2*3）+…… 1/[n*（n+1）]
=1-1/2+1/2-1/3+1/3-1/4…… +1/n-1/(n+1)=1-1/(n+1)
=>n+1=2006
So n = 2005