(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1999-1/2000)=
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![(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1999-1/2000)=](/uploads/image/z/638194-58-4.jpg?t=%EF%BC%881-1%2F2%29%2B%281%2F2-1%2F3%29%2B%281%2F3-1%2F4%29%2B.%2B%281%2F1999-1%2F2000%29%3D)
(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1999-1/2000)=
(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1999-1/2000)=
(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1999-1/2000)=
1999/2000
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=1-1/2000
=1999/2000