In this blog I found a curious limit that involves the Fibonnaci sequence and the number $ \pi$.
$$\lim\limits_{x\to \infty} \frac{\sum\limits_{i=0}^{x}log F_i}{log (lcm \left \{ F_i \right \}_{i=0}^{x })}=\dfrac{\pi^2}{6}$$
In the case of the limit is correct, Could anyone give me some pointers about the demo?
Thank you very much in advance.
