It is a very well known mathematical fact that the limiting ratio of consecutive terms of the Fibonacci sequence [F₀=0, F₁=1, F_n=F_n-1+F_n-2] is φ=(1+√5)/2 as n→∞.

Suppose we generalize the definition of the sequence to:
F_n=AF_n-1+BF_n-2.

Find an expression for the limiting ratio of consecutive terms (in terms of A and B.)

Find formulas for A and B to make the limiting ratio any whole number N.