Real Analysis: Sequences and Series for Competitive Exams

Understanding real analysis is the cornerstone of advanced mathematics, yet mastering sequences and series often feels daunting when preparing for rigorous competitive exams. This text-based course guides you from fundamental definitions to complex convergence tests, building the mathematical rigor needed to solve exam-level problems with confidence. What you'll learn: 1. Understand the core concepts of bounded, monotonic, and Cauchy sequences. 2. Apply key convergence tests for infinite series, including the ratio, root, and comparison tests. 3. Analyze limit points, limit superior, and limit inferior of real sequences. 4. Practice constructing rigorous epsilon-N proofs for sequence convergence. 5. Master problem-solving strategies to tackle sequence and series questions from major mathematics exams. 6. Explore absolute and conditional convergence of alternating series. Starting with foundational definitions of real numbers and basic set theory, this course progresses systematically through advanced convergence theorems and rigorous proof techniques. It is designed for undergraduate mathematics students and exam aspirants who want to build a strong theoretical foundation. No advanced prerequisites are required. Begin reading today to build a rock-solid mathematical foundation and boost your exam readiness.