Item 2.

Inductive case: Prove that \(P(k) \imp P(k+1)\) for all \(k \ge 0\text{.}\) That is, prove that for any \(k \ge 0\) if \(P(k)\) is true, then \(P(k+1)\) is true as well. This is the proof of an if … then … statement, so you can assume \(P(k)\) is true (\(P(k)\) is called the inductive hypothesis). You must then explain why \(P(k+1)\) is also true, given that assumption.