若[1+3+5+…+(2x-1)]÷{[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]}=110

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若[1+3+5+…+(2x-1)]÷{[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]}=110

若[1+3+5+…+(2x-1)]÷{[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]}=110
若[1+3+5+…+(2x-1)]÷{[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]}=110

若[1+3+5+…+(2x-1)]÷{[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]}=110
[1+3+5+…+(2x-1)]÷{[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]}=110
令A=1+3+5+…+(2x-1)=2x*x/2=x^2
令B={[1÷(1×2)]+[1÷(2×3)]+…+[1÷x(x+1)]
=1/1*2+1/2*3+...+1/x(x+1)
=1-1/2+1/2-1/3+...+1/x-1/(x+1)
=1-1/(x+1)
=x/(x+1)
所以原式 A/B=110
即 x^2/[x/(x+1)]=110
x(x+1)=110
x^2+x-110=0
x1=10 x2=-11(舍去)
所以x=10

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