perplexus.info :: Calculus : Sum ArcTan Limit

Sum ArcTan Limit (Posted on 2016-05-11)

F(k) denotes the kth Fibonacci Number.

Define:
G(n) = Σ_{k=1 to n} ArcTan((F(2k+1)^-1)

Find:
Limit G(n)
n → ∞

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 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 |

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

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:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info