Remember that the Fibonnaci Sequence is the sequence described by f(0)=1, f(1)=1, with f(n) = f(n-1) + f(n-2). We are interested in the the ratio f(n+1)/f(n). Let's call the the ratio
We can assume that the limit of xsub n as n approachs infinity is x.
So,
Since we are dealing only with positive values of x,
which equals the golden ratio 1.618033988738303.