1/(1x2)+1/(2x3)+1/(3x4)+.+1/(2011x2012) 【运用：1/[n(n+1)]=1/n-1/(n+1)】=(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【中间的都约掉了】...