1. Prove the following propositions using mathematical induction. a. 5 points In Calculus, the chain rule allows you to calculate the derivative of a function composed of two other functions. Prove the following special case of the chain rule, for all n > 1: The only fact about derivatives that you need to know (and the only one you are allowed to use in your proof) is the product rule: b. [5 points] Let an be the recursive sequence defined by ao Prove that Tl ai-2+3an ->an+1 2 for all n 0