note that f_n = (a^n + b^n) / sqrt(5) ~ a^n / sqrt(5) the denominator is important. also another interesting relation is a^n ~ f_(n+1) + f_(n-1) = f_(n+2) -

note that f_n = (a^n + b^n) / sqrt(5) ~ a^n / sqrt(5) the denominator is important. also another interesting relation is a^n ~ f_(n+1) + f_(n-1) = f_(n+2) - f_(n-2)