Sequence and Series for Competitive Mathematics and IIT JAM

Succeeding in competitive mathematics exams requires a rock-solid understanding of real analysis fundamentals. This course simplifies complex mathematical theories, helping you build a strong analytical foundation from scratch. You will progress from basic definitions to solving sophisticated problems with confidence. By working through this comprehensive text-only guide, you will transition from memorizing formulas to deeply understanding the behavior of sequences and series. You will learn to identify convergence, apply rigorous mathematical tests, and tackle exam-style questions systematically. What you'll learn: - Understand foundational concepts of real sequences, bounds, and limit points - Apply convergence tests including the Ratio, Root, Integral, and Comparison tests - Master the behavior of alternating series and determine absolute versus conditional convergence - Solve complex limits using Cauchy's theorems and squeeze principles - Practice step-by-step problem-solving techniques tailored for competitive mathematics exams The course begins with essential terminology, basic definitions, and the core properties of real numbers. It then guides you through structured text lessons and detailed mathematical proofs, culminating in practical strategies for solving exam-level questions. This course is designed for beginners starting their exam preparation journey, as well as students looking to reinforce their mathematical analysis skills. No advanced prerequisites are required, though a basic familiarity with high school calculus is helpful. Start reading today to master sequence and series for your upcoming exams.