Advanced Sequence and Series for Mathematics Admissions Exams

Succeeding in competitive mathematics admissions exams requires a deep, intuitive understanding of real analysis fundamentals. This text-based course is designed to take your mathematical reasoning to the next level by demystifying complex convergence behaviors and series properties. You will transition from basic calculation to rigorous mathematical proof and analysis. What you'll learn: Understand foundational definitions of bounded sequences, limits, and convergence criteria; Apply key convergence tests including the ratio, root, integral, and comparison tests; Master advanced concepts such as Cauchy sequences, subsequence behavior, and absolute convergence; Analyze alternating series and apply Leibniz's test with confidence; Practice solving complex multiple-choice and analytical problems typical of competitive exams. The course begins with a thorough review of fundamental definitions and real number properties before advancing to rigorous proofs, limit evaluations, and exam-style practice problems. This course is designed for mathematics students and aspirants preparing for competitive university entrance exams who have a basic background in calculus. Start mastering sequence and series theory today to secure your academic future.