作业帮2/3+[3/(1+2)*(1+2+3)]+[4/(1+2+3)*(1+2+3+4)]+…+[18/(1+2+3+…+17)*(1+2+…+18)
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2/3+[3/(1+2)*(1+2+3)]+[4/(1+2+3)*(1+2+3+4)]+…+[18/(1+2+3+…+17)*(1+2+…+18)
2/3+[3/(1+2)*(1+2+3)]+[4/(1+2+3)*(1+2+3+4)]+…+[18/(1+2+3+…+17)*(1+2+…+18)
2/3+[3/(1+2)*(1+2+3)]+[4/(1+2+3)*(1+2+3+4)]+…+[18/(1+2+3+…+17)*(1+2+…+18)
题目里的每个大括号里面的分式可以这样化简
例如,
3/(1+2)*(1+2+3)=1/(1+2)-1/(1+2+3),
……
18/(1+2+3+…+17)*(1+2+…+18)=1/(1+2+3+…+17)-1/(1+2+3+…+17+18)
所以原式=
2/3+[1/(1+2)-1/(1+2+3)]+[1/(1+2+3)-1/((1+2+3+4)]+……+[1/(1+2+3+…+17)-1/(1+2+3+…+17+18)]=2/3+1/3-1/(1+2+3+…+17+18)=170/171
2 1 -2 -3
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1+1+2+2+3+3+````````````````````````````+99999
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