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x/1*2+x/2*3+x/3*4+…+x/99*100=1 x(1/1*2+1/2*3+1/3*4+…1/99*100)=1 x(1-1/2+1/2-1/3+1/3-1/4+…+1/99-1/100)=1 x(1-1/100)=1 x=100/99
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