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1/5*1/6+1/6*1/7+1/7*1/8+1/8*1/9+1/9*1/10=1/10...

拆分每个分数。记住等式: 1/(x(x+1))=1/x-1/(x+1) 所以,原等式就可以简化为1/1-1/10=0.9

解:1/(4×5×6)=1/2[1/(4×5)-1/(5×6)] 1/(5×6×7)=1/2[1/(5×6)- 1/(6×7 )] 1/(6×7×8)=1/2[1/(6×7)- 1/(7×8)] ……… 1/(98×99×100)=1/2[1/(98×99)-1/(99×100)] ∴1/(4×5×6)+ 1/(5×6×7)+ 1/(6×7×8)+…..+ 1/(98×99×100) =1/2[1/(4×5)-1/(5×6)]+ 1/2[1/(5...

注意:1/2是0,1.0/2结果才是0.5。同样-1/4,1/5都是0,希望可以帮到你。

原式=1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12

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