1. Prove the Strong Principe of Mathematical Induction. Let P(n) be an open statement over the domain 220.. If 1) P(d) is true 2) the implication If PU) for every integer i with d 5 1' 5 k, then P(k + l). is true for every integer k E Z20: then P(n) is true for all n 6 22d. 2. Let a E 22 be an odd integer. Prove that a\" is odd for all positive integers n. 1 1 1 3. Provethat++---+= n f H . 1-2 2-3 n(n+1) n+1ra \"EN . 4 4 4 (n + 1X\" + 2) - > ' _ _ _ _ . . n = 4 Prove that for every Integer n _ 3 (l 32) (1 42) (1 n2) 6n(n _ 1) 5. Prove that n! > 2\" for every integer n 2 4. 6. Let X E R and X > 1. Prove that (1 + X)\" Z 1 + nx for every positive integer n. 7. Use induction to prove that 3 | (22\" 1) for all nonnegative integers n