**Title:** Elementary Math Challenges in Induction and Recurrences

**Speaker:** Miguel A. Lerma

**Speaker Info:** Northwestern University

**Brief Description:** Training session for the Putnam Competition.

**Special Note**: **Training session for the Putnam Competition.**

**Abstract:**

Mathematical Induction is a mathematical proof technique used to prove that a property \(P(n)\) holds for every natural number \(n\), i.e. for \(n = 0, 1, 2, 3,\) and so on. The idea is to prove a base case \(P(0)\), and then prove the induction step \(P(n)\) implies \(P(n+1)\). We will look at various applications of this technique.A recurrence is a description of a function or sequence in terms of itself. A well known example is the Fibonacci sequence \(F_{n+2} = F_{n+1} + F_{n}\) for \(n \geq 0\), with initial conditions \(F_{0} = 0\), \(F_{1} = 1\). Some challenging problems can be naturally posed and solved using recurrences.

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