Real Analysis: Sequences of Real Numbers for Competitive Exams

Succeeding in advanced mathematics exams requires a rock-solid grasp of real analysis, starting with how sequences behave. This text-based course guides you from the absolute basics of real numbers to complex convergence tests, helping you build the analytical skills needed to solve exam-style problems with confidence. What you'll learn: - Understand foundational definitions of sequences, bounds, and monotonicity - Apply key convergence tests including the Squeeze Theorem and Monotone Convergence Theorem - Calculate limits of sequences using algebraic properties and limit laws - Analyze subsequences, limit superior, and limit inferior in various mathematical contexts - Practice rigorous proof techniques and step-by-step problem-solving strategies You will start by exploring core terminology and basic properties of real numbers before moving into detailed convergence criteria and practical, written exam-focused exercises. This course is designed for beginners and students preparing for competitive mathematics exams, with no prior advanced analysis experience required. Start reading today to master the core principles of real sequences.