Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2, an = an−1 + an−2 . a. Show that f(x) = 1 1−x−x 2 is the generating function of the Fibonacci Sequence. b. Find and β such that 1 − x − x 2 = (1 − x)(1 − βx). c. Find A and B in terms of and β, such that 1 1−x−x 2 = A 1−x + B 1−βx. d. Use the results of the previous parts to obtain a formula for an.