1/1x2+1/2x3+1/3x4+```````+1/1999x2000=?

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1/1x2+1/2x3+1/3x4+```````+1/1999x2000=?

1/1x2+1/2x3+1/3x4+```````+1/1999x2000=?
1/1x2+1/2x3+1/3x4+```````+1/1999x2000=?

1/1x2+1/2x3+1/3x4+```````+1/1999x2000=?
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1998-1/1999)+(1/1999-1/2000) =1-1/2000=1999/2000

1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+......+1/(1999x2000) =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....-1/1998+1/1998-1/1999+1/1999-1/2000 =1-1/2000 =1999/2000 希望帮到你o(∩_∩)o 不懂追问哦