1/(x+1)(x+2)+1/(x+2)(x+3).+/(x+2011)(x+2012) =1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3).+1/(x+2011)-1/(x+2012) =1/(x+1)-1/(x+2012) =2011/(x+1)(x+2012)