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

Home > Just Math
Sum Square Roots ≤ Real Number (Posted on 2010-04-10) Difficulty: 3 of 5
Determine all possible value(s) of a positive integer constant c that satisfy this relationship:

√(y-1) + √(y-2) + .....+ √(y-c) ≤ y

whenever y is a positive real number ≥ c

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: by graphing -- more thoughts | Comment 2 of 4 |
(In reply to by graphing by Charlie)

While increasing c, as soon as you have violations, at particular c and y, if you, say double both c and y, there will be twice as many terms on the left and the terms will be approximately multiplied by sqrt(2) so the LHS increases as the 1.5 power of the common factor of increase of y and c, while the RHS increases as only the 1st power, so the violations will be getting worse as you increase c. This is evidence that indeed 1 and 2 are the only values of c that work.
  Posted by Charlie on 2010-04-10 16:04:00

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