1/1X2X3+1/2X3X4+1/3X4X5+...+1/98X99X100(要过程)

如题所述

第1个回答 2013-09-09

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.本回答被网友采纳

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1/1X2X3+1/2X3X4+1/3X4X5+...+1/98X99X100(要过程)答：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.

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