5. (5.4.8) Consider the sum of the first n positive integers. For example, given n = 4: =1+2+3+ 4 ...the sum of the first 4 positive integers is 10. (a) Give pseudocode for a recursive algorithm that computes the sum of the first n positive integers. (b) State a lemma that you would need to prove in order to show the correctness of your algorithm. (c) Prove that your algorithm is correct. 1 of 2