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

Home > Numbers
Power to the 2 (Posted on 2004-02-20) Difficulty: 2 of 5
What is the limit to this sequence?

√(2)
√(2+√(2))
√(2+√(2+√(2)))
√(2+√(2+√(2+√(2))))...

In general, what is the sequence in terms of x if 2 is replaced with x?

See The Solution Submitted by Gamer    
Rating: 2.8750 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Nice | Comment 3 of 10 |
If we call S the 'n' term of this sequence, like:
S = √(2+√(2+√(2+...
and we square both sides of the equation, we will reach:
S² = 2+S
S²-S-2=0
S=(1(+/-)√(1+2*4))/2, and considering only the positive solution as valid for our purpose, we reach S=2 as being the limit to this sequence.
And if 2 is replaced with X, the solution would be S=((1+√(1+4*X))/2 (again considering only the positive solution as valid for us).
  Posted by Roberto Mattos on 2004-02-20 12:29:14
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 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information