g Prove that ∀n ∈ N, Pn i=0 2 i = 2n+1−1 (in other words, 1+2+4+8+· · ·+ 2 n = 2n+1 − 1). Use the following proof strategy: Proof by contradiction. Take the set of all n for which this statement is false. Use the fact that every set of non-negative integers has a minimum. Call that minimum k. Either k = 0 or the statement is true for k − 1. Get a contradiction from here.