4. For the following two problems use induction to prove. Recall the standard definition of the Fibonacci numbers: F, = 0, F1 = 1 and En Fn-1 + Fn-2 for all n > 2. a. Prove that F; i= Fn+2 - 1 for every non-negative integer n. (10 Points] b. The Fibonacci sequence can be extended backward to negative indices by rearranging the defining recurrence: Fn = Fn+2 Fn+1. Here are the first several negative-index Fibonacci numbers: n -9 -8 -4 -10 -7 -6 -5 Fn 34 -21 13 -8 5 Prove that F-n = (1)n+1 Fn for every non-negative integer n. -3 2 -2 -1 -1 1 -55 -3 (10 Points]