In a Fibonacci sequence 1, 1, 2, 3, 5, …, F_n, F_n+1
define R_n = F_n/ F_n-1

Prove that lim (R_n) as n approaches infinity
is .5*(1+sqrt(5))=1.618...
a.k.a. the golden ratio, φ (phi).

(In reply to Solution by JayDeeKay)

This proof is only half done.  JayDeeKay has proved that if there is a limit it must be the Golden Ratio.  But it has not been proved that there is in fact a limit.  

Posted by Steve Herman on 2015-09-16 12:28:30