2. (25 points) The Fibonacci numbers Fo, F1,..., are defined by Fo 0, F11, Fn = Fn-1 + Fn-2 Use induction to prove that: (a) Use induction to prove that Fn 20.5n for n 6 (b) Use induction to prove that Fn 2 for n 0 (c) Based on the previous parts, write an upperbound of Fr using O notation and a lower bound using notation.