根据式子n(n+1)分之1=n(n+1)分之（n+1)-n=n分之1-n+1分之1计算1x2分之1+2x3分之1+3x4分之1+...+2011x2012分之1

1/(1*2)+1/(2*3)+1/(3*4)+.1/(2011*2012)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2011-1/2012)
=1-1/2+1/2-1/3+1/3-1/4+.+1/2011+1/2012
=1-1/2012
=2011/2012