4 is previous question

4. Here is a "proof" that T-(2-1) = n2 + 1 for n 2 1. Set up the variables: For each k > 1, let All be true if (21-1) = he? +1. Induction step: We need to show that for all k > 1, Ax- > All If AR-1 is false, the implication is immediately true. Let's show that it must be true by supposing that A-1 is true and showing can't be false in this case either. If As-, is true, then = (2-1) = (k: - 1)2 +1. Then -1 = (k-1)2 +1+(2k-1) = (k2 - 2k + 1) + 1 + 2k-1=k? +1. Notice that we have forgotten about the base case. For each of the following state- ments, tell whether we have proved the statement true: 5. On the previous problem, an obstacle is that the claim is false. In fact, (2-1) = n. For example, when n = 4, 1-(21 - 1) = 1+3+5+ 7 = 16 = 42. Reproduce the above proof, making appropriate alterations, so that it proves that that I 1(21 - 1) = nfor all n > 1