For Problems 1-5, prove the statements by mathematical induction. Clearly state your basis step and prove it. What is your inductive hypothesis? Prove the inductive step and show clearly where you used the inductive hypothesis (assumption). 1. [5 Pts] 13+ 23+ .. . + n3 = (n(n + 1)/2)), for all positive integers n. 2. [5 Pts] 1 . 1! + 2 . 2! + . . . + n . n! = (n + 1)! -1, for all positive integers n. 3. [5 Pts] 2 - 2 - 7 + 2 -72 -... + 2(-7)" = (1 -(-7)"+1)/4, for all non-negative integers n