1.a) Let P(n) denote 1 + 2 + 2² + .... + 2ⁿ = 2^{n + 1} - 1 . Using mathematical induction show that P(n) is true for all nonegative integers (this includes 0).

b) Give a recursive definition with initial condition(s) of the set S = {0, 3, 6, 9,...}