The numbers F0, F1, F2,... are defined as follows (this is a definition by mathematical induction, by the way): F0 = 0, F1 = 1, Fn+2 = Fn+1 + Fn for n = 0,1,2,....... Prove that for any n>=0 we have Fn<=((1 + sqrt5)/2)^(n-1)

Plz give a counting prof instead of induction.