This is a practice question from my Data Structures course: h(n) = {1 if n = 1; 3 × h(n - 1) - 1 otherwise} Rewrite h(n) using an explicit formula that is not recursive (i.e., succinctly express h(n) as a polynomial/exponential function of n). Also, prove the correctness of your expression using mathematical induction. Please explain how to do this (as opposed to simply providing the answer).

This is a practice question from my Data Structures course: h(n) = {1 if n = 1; 3 × h(n - 1) - 1 otherwise} Rewrite h(n) using an explicit formula that is not recursive (i.e., succinctly express h(n) as a polynomial/exponential function of n). Also, prove the correctness of your expression using mathematical induction. Please explain how to do this (as opposed to simply providing the answer).