Reciprocal Fibonacci constant

chiph588 19 Nov 2008 19:30

Let $F_k$ be the $k$th Fibonacci number.

Define

(1)\begin{align} \psi = \sum_{k=1}^{\infty} \frac{1}{F_k} \approx 3.359885666243177553172011302918927179688905133731 \ldots \end{align}

the sum of the reciprocals of every Fibonacci number

It has been proved to be irrational which looks like a daunting task to me

heres a link for more info:

http://en.wikipedia.org/wiki/Reciprocal_Fibonacci_constant