perplexus.info :: Numbers : The Great Comparison

The Great Comparison (Posted on 2019-03-02)

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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

| Comment 2 of 6 |

Let x = 10^2017 + 1. Then A=(200x+1)/(x^2+2x+5) and B=(200x)/(x^2+2).

A-B = [-399x^2-600x+2]/[(x^2+2+5)*(x^2+2)]. This is obviously negative when x = 10^2017 + 1, therefore B is greater.

Posted by Brian Smith on 2019-10-26 20:54:12

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info