Doctor John wrote:
> Is there anywhere an elegant proof that Phi**n = F(n-1) + [F(n) * Phi]
> where F(x) is the value of the Fibonacci number x and Phi is the "Golden
> ratio" defined as Phi**2 - Phi - 1 = 0. I can demonstrate it with ease
> for an arbitrary value of n, but I seem to have forgotten the proof for
> all values of n. (BTW ** is the standard "raise to the power of"]

Since F(n) = ( phi^n - (1-phi)^n ) / sqrt(5), just plug in the formula 
for F(n) into your lemma equation and you'll have your proof.

Regards,
John

Post a reply to this message