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

Home > Numbers
The 1234 Problem (Posted on 2013-09-05) Difficulty: 1 of 5
The following factorizations of numbers are true:
Can this scheme be continued infinitely?

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 1 of 1

let x=sum(10^k,k=0 to n-1)=(10^n-1)/9
then the left hand side is
the right hand side is
where n is the number of 1's appearing on the left side

Now substituting in the equation for x=(10^n-1)/9 and simplifying we get on the left side
on the right side
9*(10^n-1)^2/81 + 3*(10^n-1)/9
thus the left and right hand sides simplify to the same equation and thus it holds for all n

  Posted by Daniel on 2013-09-05 11:19:23
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information