1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=

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1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=
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1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=
1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=

1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=
1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100
=(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+...+(1/2)(1/98*99-1/99*100)
=(1/2)*(1/1*2-1/2*2+1/2*3-1/3*4+...+1/98*99-1/99*100)
=(1/2)*(1/2-1/9900)
=(1/2)*(4949/9900)
=4949/19800.

题目应为:1/(1*2*3)+1/(2*3*4)+...+1/(98*99*100)
原式=1/2*(1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+...+1/(98*99)-1/(99*100))=4949/19800