Please provide proof in paragraph form

Problem 1. (40 points) Let f0, f1, f2, . .. be the Fibonacci sequence dened in zyBooks (f0 = 0, f1 = 1, and for every I: > 1, fk = fk_1 + fk_2). This problem will help us understand how quickly this sequence grows. In each of the following parts, you can use previous parts, even if you haven't solved them. a) (20 points) Use induction to prove that for all n 2 0, f0 + f1 + - - - + fn = fn+2 1. (Note that this is quite similar to how powers of 2 add up to almost the next one) b) (20 points) Use strong induction to prove that for every n 2 2, fn 2 (1.5)"_2. Hints: 0 You'll need two base cases, f2 and f3. 0 For the inductive case of fk+1, you'll need to use the inductive hypotheses for k and k 1. 0 Keep in mind that 2.25 = 1.52. It might help you somewhere in the proof