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

Home > Just Math
Spacy Colors Lemma (Posted on 2014-12-06) Difficulty: 4 of 5


Let { ak } be any sequence of real numbers that satisfies
   ak ≥ ak+1 > 0 for all k≥1.
Let { rk } be the sequence of real numbers that satisfies
   rk = ak                        for k = 1,

      = ak*√[ 1 - tk*tk ]          for k > 1,

   where tk = ak/(2*rk-1).
Clearly, for all k > 1, rk is defined and greater than zero
if tk∈(0,1).

Prove or disprove that tk∈(0,1) for all k > 1.

See The Solution Submitted by Bractals    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
There are no comments yet.
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 (1)
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