Prove the following statements with either induction, strong induction, or proof by smallest counterexample: a. Concerning the Fibonacci sequence, prove that the summation from k =1 to n of (Fk)^2 = Fn * Fn + 1 b. Prove that 3^1 + 3^2 + 3^3 + 3^4 + ... + 3^n = [3^(n + 1) - 3]/2 for every integer n. c. Prove that if n, and k are integers and n is even and k is odd, then n!/k!(n - k)! is even. d. Prove that the nth fibonacci number Fn is even if and only if 3 | n

 Prove the following statements with either induction, strong induction, or proof by
 smallest counterexample:

a. Concerning the Fibonacci sequence, prove that the summation from k =1 to n of (F_k)^2 = F_n * F_{n + 1}

b. Prove that 3^1 + 3^2 + 3^3 + 3^4 + ... + 3^n = [3^(n + 1) - 3]/2 for every integer n.

c. Prove that if n, and k are integers and n is even and k is odd, then n!/k!(n - k)! is even.

d. Prove that the nth fibonacci number F_n is even if and only if 3 | n