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The Great Comparison (Posted on 2019-03-02) Difficulty: 3 of 5
A = 200..002/(100..0022 + 2)
B = 200..001/(100..0012 + 2)

Both the number expressions have 2019 zeros in the numerator and 2017 zeros in the denominator.

Which of the two numbers is greater?

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Solution | Comment 3 of 6 |
(In reply to Solution by Brian Smith)

Sorry, but I could not reproduce the algebra used for your substitutions involving "x". So, I tried an example. Instead of the 19 and 17 zeros, I went for 4 and 2 zeroes, and I made x correspondingly scaled:

x = 10^2 + 1

The new A and Bs don't agree with the old ones. 

rabbit-3:~ lord$ more v.f

        program v

        x=10**2+1

        a=200002./(1002.**2+2)

        b=200001./(1001.**2+2)

        a1=(200*x+1)/(x**2+2*x+5)

        b1=200*x/(x**2+2)

        print*,'a a1 ',a,a1

        print*,'b b1 ',b,b1

        end

rabbit-3:~ lord$ v

 a a1   0.199203983       1.94091082    

 b b1   0.199601203       1.97980988  

I changed x to produce the needed number of zeroes and still got disagreement as the LSD gets shifted up: 

        x=10**3+1

rabbit-3:~ lord$ v

 a a1   0.199203983      0.199401796    

 b b1   0.199601203      0.199799806    

Edited on October 27, 2019, 3:11 pm
  Posted by Steven Lord on 2019-10-27 15:00:13

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