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

Home > Just Math > Calculus
Sum ArcTan Limit (Posted on 2016-05-11) Difficulty: 3 of 5
F(k) denotes the kth Fibonacci Number.

Define:
G(n) = Σk=1 to n ArcTan((F(2k+1)-1)

Find:
Limit G(n)
n → ∞

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): summing the series via computer | Comment 3 of 6 |
(In reply to re: summing the series via computer by ken)

The first F I'm accounting for is F(3), as k=1 produces F(3).


Thereafter, the duplicated lines:

   f1 = f2: f2 = f3: f3 = f1 + f2
   f1 = f2: f2 = f3: f3 = f1 + f2

each advance by one F number, so together they advance to the next odd-numbered F.

So, yes, it counts only the odd-numbered Fibonaccis, and also excludes F(1).

  Posted by Charlie on 2016-05-11 14:45:20
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