4. Suppose we wanted to use mathematical induction to prove that for each natural number n, 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1). What would we show in the base step for n = 1 and n = 2? None of these are correct. We would show that if the statement is true for the first k elements, then it is true for the (k + 1)st element. We would show that the statement was true for n = 1 and for n = 2 by plugging 1 and 2 into our formula separately, and making sure they both make a true statement. We would show that 2 - 1 = 1. 5. Suppose we wanted to use mathematical induction to prove that for each natural number n, 2 + 5 + 8 + ... + (3n - 1) = n(3n - 1) / 2. In our induction step, what would we assume to be true and what would we show to be true. Assume: 2 + 5 + 8 + ... + (3k - 1) + (3(k +1) - 1) = (k + 1)(3(k+1) - 1) / 2 Show: 2 + 5 + 8 + ... + (3k - 1) = k(3k - 1) / 2 None of these are correct. Assume: 2 + 5 + 8 + ... + (3k - 1) = k(3k - 1) / 2 Show: 2 + 5 + 8 + ... + (3k - 1) + (3(k +1) - 1) = (k + 1)(3(k+1) - 1) / 2 Assume: 2 - 3 - 8 - ... - (3k + 1) = 3k / 2 Show: 2 - 3 - 8 - ... - (3(k - 1) - 1) = 3(k + 1) / 2