Use mathematical induction to show that 32\" 1 is divisible by 8 for all natural numbers 11. Let P(n) denote the statement that 32" 1 is divisible by 8. P(1) is the statement that 3:] 1 = C] is divisible by 8, which is true. Assume that P(k) is true. Thus, our induction hypothesis is is divisible by 8. We want to use this to show that P(k + 1) is true. Now, 32(k+:])_1 = 9(3l:lk)_1 = 9(3l:lk):l+8 9(3ZK_E)+8. This final result is divisible by 8, since is divisible by 8 by the induction hypothesis. Thus, P(k + 1) follows from P(k), and this completes the induction step. Having proven the above steps, we conclude by the Principle of Mathematical Induction that P(n) is true for all natural numbers n. Use mathematical induction to determine which of the following is divisible by 3 for all natural numbers n. (Select all that apply.) On(n - 1) + 3 On(n - 1)(n + 1) + 87 On ( n2 - 1 ) + 3 On2 + 3n + 88 On2 + 3n - 2Use mathematical induction to determine which of the following is divisible by 4 for all natural numbers n. (Select all that apply.) 0 7 +1 0 57 + 1 - 13 0 37 + 1 O 107 - 2 67 - 2 X