1/(1×2)=1-1/21/(2×3)=1/2-1/31/1x2+1/2x3+1/3x4+…+1/2010x2011 =1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011=1+(1/2-1/2)+(1/3-1/3)+...+(1/2010-1/2010)-1/2011=1-1/2011=2010/2011裂项求和