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?

I did a little more cleanup. It is a nice straight-forward proof.

let x = 10^2018.  

Then A=(200x+2)/(x^2+4x+6) and B=(200x+1)/(x^2+2x+3).

A-B = [-399x^2-596x]/[(x^2+4x+6)*(x^2+2x+3)]. 

 This is obviously negative when x=10^2018, therefore B is greater.

Edited on October 27, 2019, 7:04 pm

Posted by Steven Lord on 2019-10-27 19:04:23