Understanding Mathematical Induction
Mathematical induction (aka Principle of Mathematical Induction) is a powerful technique in mathematics used to prove statements that are true for infinitely many natural numbers. Formally, the principle of mathematical induction is stated as:
For \(n \in \mathbb{N}\), let \(P(n)\) be a predicate. If
Base Case: \(P(0)\) is true, and Inductive Step: Assuming \(P(n)\) is true show \(P(n) \implies P(n + 1)\) holds.…