1/1x2+1/2x3+.1/2010x2011=?

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1/1x2+1/2x3+.1/2010x2011=?1/1x2+1/2x3+.1/2010x2011=?1/1x2+1/2x3+.1/2010x2011=?1/(1×2)=1-1/21/(2×3)=1

1/1x2+1/2x3+.1/2010x2011=?
1/1x2+1/2x3+.1/2010x2011=?

1/1x2+1/2x3+.1/2010x2011=?
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

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

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

2010/2011

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