Prove the given property of the Fibonacci numbers for all n => 1 (Hint: the first principle of induction will work and use the definition of the Fibonacci numbers in the proof). Justify each step. [F(1)]^2+[F(2)]^2+:::+[F(n)]^2 = F(n)F(n+1)

1. Prove the base case

2. What is the inductive hypothesis P(k)?

3. Show what you have to prove, that is P(k+1)

4. Prove P(k)->P(k + 1) (justify each step)