5. (15 points) What is the error in the following "proof" for the wrong statement n2 -O(n)? We use induction on n. The base case n = 1 is trivial as obviously 1 = 0(1). To use induction consider the induction hyopthesis n2- O(n). To make the induction work, we need to prove that the induction hypothesis implies (n1)2 O(n +1). But indeed this is easy as (n + 1)2 = n2 2n + 1 0(n) + 2n + 1 = 0(n + 1), where the second equality uses the induction hypothesis n2 O(n)