1/x(x+1)+……+1/(x+2011)(x+2012)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+2011)-1/(x+2012)
=1/x-1/(x+2012)
=2012/(x²+2012x)
=6036/(3x²+6036x)
=6036/2
=3018