4. For the following two problems use induction to prove. Recall the standard definition of the Fibonacci numbers: F0=0,F1=1andFn=Fn1+Fn2foralln2. a. Prove that i=0nFi=Fn+21 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+2Fn+1. Here are the first several negative-index Fibonacci numbers: Prove that Fn=(1)n+1Fn for every non-negative integer n. [10 Points]