More about Fibonacci Numbers
Consider a generalized Fibonacci sequence, G0, G1, G2, G3, G4,..... Suppose we imagine that there is a number x such that G0 = 1 G1 = x G2 = x^2 G3 = x^3 G4 = x^4 etc Is such an x possible? The only requirement is that G2 = x^2 G2 = G0 + G1 x^2 = 1 + x Multiply through by x. x^3 = x + x^2 G3 = G1 +... Sign in to see full entry.