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所有问题
1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=
如题所述
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其他回答
第1个回答 2008-03-29
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.本回答被提问者采纳
第2个回答 2008-03-29
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
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答:
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/
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.
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