1⼀1x2+1⼀2x3+1⼀3x4+…+1⼀2010x2011 讲解一下！ 知道答案但看不明白啊！怎么办，求各位老大讲解一下吧！

1/(1×2)=1-1/2
1/(2×3)=1/2-1/3
1/1x2+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

1/2x2可以写成1-1/2，1/2x3可以写成1/2-1/3...依次类推，最后化成的分数+1/2与-1/2抵消，-1/3与+1/3抵消，以此类推，最后抵消成1-1/2011，所以结果为1/2010.

1/(1*2)=(2-1)/(1*2)=1/1-1/2
1/(2*3)=(3-2)/(2*3)=1/2-1/3
1/(3*4)=(4-3)/(3*4)=1/3-1/4

...
1/(2010*2011)=(2011-2010)(2010*2011)=/1/2010-1/2011
上式相加，
得1/1x2+1/2x3+1/3x4+…+1/2010x2011=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2010-1/2011)
=1-1/2011
=2010/2011

1/1x2+1/2x3+1/3x4+…+1/2010x2011
=1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011
=1-1/2011
=2010/2011 .

1/1x2+1/2x3+1/3x4+…+1/2010x2011
=1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011
=1-1/2011
=2010/2011