Sequences and Series for IIT-JAM and College Mathematics

Mastering the behavior of sequences and infinite series is one of the most critical steps for succeeding in advanced calculus and competitive mathematics. This comprehensive, text-only course is designed to take you from basic definitions to the rigorous limit theorems and convergence tests required for university-level exams. You will build a deep, intuitive understanding of real analysis concepts through clear written explanations and structured mathematical proofs. What you'll learn: - Understand the fundamental concepts of bounded, monotonic, and Cauchy sequences. - Apply key convergence tests including the ratio, root, integral, and comparison tests to infinite series. - Master the properties of limits, subsequences, and the squeeze theorem for solving complex limit problems. - Analyze alternating series and determine absolute versus conditional convergence. - Practice systematic problem-solving strategies tailored for competitive mathematics entrance exams. The course begins with foundational definitions of real sequences, ensuring you have a strong grasp of the terminology before advancing to limit theorems. You will then progress through detailed written analyses of infinite series, convergence criteria, and practical exam-style problem sets. This course is ideal for undergraduate mathematics students and aspirants preparing for competitive entrance exams who want to master real analysis from the ground up. Start reading today to elevate your mathematical reasoning and build exam-day confidence.