Sequence and Series in Real Analysis for Mathematical Exams

To excel in higher mathematics and competitive exams, you must have a rock-solid grasp of real analysis. This text-based course is designed to take you from foundational definitions to advanced problem-solving with sequences and series of real numbers. You will develop the logical precision required to understand, analyze, and write rigorous mathematical proofs. What you will learn: Understand the core definitions of sequences, bounded terms, and limit points; Apply convergence tests such as the ratio, root, comparison, and integral tests; Master the properties of power series, radius of convergence, and uniform convergence; Practice solving exam-style proof problems step-by-step; Explore modern applications of real analysis in computational algorithms and data science models. This comprehensive text-only program starts with basic terminology and foundational axioms before guiding you through structured proofs and advanced convergence behavior. This course is designed for undergraduate mathematics students, aspiring researchers, and candidates preparing for rigorous competitive exams in mathematics. Start reading today to build your analytical foundations and master real analysis.