Linear Recurrence Relations: Solving Techniques

This lecture covers linear homogeneous recurrence relations, including their definitions, terminology, examples, and characteristic equations. It explains how to solve these relations using strong induction, characteristic roots, and initial conditions. The instructor demonstrates techniques for solving linear homogeneous recurrence relations of degree two with constant coefficients, as well as relations with repeated roots. The lecture concludes with examples, such as Fibonacci numbers, and general linear recurrence relations. Students will learn the step-by-step process of determining characteristic equations, finding roots, and deriving closed solutions.