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This lecture covers the concept of limits of recursive sequences, including examples and necessary conditions for the existence of limits. It also explores the algebraic operations related to limits at infinity. The lecture discusses the convergence of sequences, the boundedness of sequences, and the process of proving the existence of limits. Additionally, it delves into the properties of sequences and the convergence to specific values. The lecture concludes with examples demonstrating the application of limits in solving equations and determining the convergence of sequences.