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 → ∞

(In reply to re(2): summing the series via computer by Charlie)

BTW, yes, of course it would make a difference to include the even Fibonaccis.  Experimenting with that finds nothing that's as remarkable as the odd numbered Fibonacci's above 1.

Posted by Charlie on 2016-05-11 14:55:30