All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
A little Generalization (Posted on 2012-12-18) Difficulty: 2 of 5
Observe that
1/1+1/3=4/3;4^2+3^2=5^2
1/3+1/5=8/15;8^2+15^2=17^2
1/5+1/7=12/35;12^2+35^2=37^2
State and prove the generalization suggested by the above examples.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 1 of 2

it would seem that you are suggesting that when you add the inverse of consecutive odd integers then resulting numerator and denominator form a pythagorean triple.  This can be show as follows:

1/(2n-1)+1/(2n+1)=
(2n+1+2n-1)/[(2n-1)(2n+1)]=
4n/(4n^2-1)
now
(4n)^2+(4n^2-1)^2=
16n^2+16n^4-8n^2+1=
16n^4+8n^2+1=
(4n^2+1)^2


  Posted by Daniel on 2012-12-18 11:13:23
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information