Can anyone help me see why this particular function seems to generate coefficients of the Fibonacci sequence when constructed in the following way:
f(x)= (x+1)/(x+2) , then ff(x) = (2x+3)/(3x+5) , fff(x) = (5x+8)/(8x+13), ffff(x) = (13x+21)/(21x+34) etc.
What is it about the original function that makes this happen? I tried explored f(x) = (x+a)/(x+b) and it started getting messy and led to an equation b^2= a+ab+1, but i am not sure that is the right approach...
f(x)= (x+1)/(x+2) , then ff(x) = (2x+3)/(3x+5) , fff(x) = (5x+8)/(8x+13), ffff(x) = (13x+21)/(21x+34) etc.
What is it about the original function that makes this happen? I tried explored f(x) = (x+a)/(x+b) and it started getting messy and led to an equation b^2= a+ab+1, but i am not sure that is the right approach...