6. The Fibonacci sequence is defined by f1 = f2 = 1, and if n 2 3, then fn = fn-1+ fn-2. The first few terms are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. For all n 2 1, define an = fn (a) Prove that an = 1 + an-1 (b) Let o = 1ty be the larger root of x2 = x + 1. Prove that if an > o, then anti o. (c) Prove that the sequence {amn } is decreasing and the sequence {a2n+1} is increasing. (d) Prove that limn +x an = 0