Foundations of Sequences and Series

Understanding how numbers progress in a predictable order is crucial for success in higher mathematics and quantitative fields. This course provides a clear, foundational introduction to sequences and series, focusing on rigorous algebraic techniques. By the end of this course, you will possess a strong grasp of sequence types, summation formulas, and the application of key inequalities, enabling you to tackle complex algebraic problems with confidence. What you'll learn: * Understand the core definitions and properties of Arithmetic Progressions (AP) and their summation formulas. * Master the characteristics and formulas for Geometric Progressions (GP), including infinite geometric series. * Apply techniques for finding the sum of complex and special series, such as arithmetic-geometric progressions. * Practice algebraic manipulation, method of differences, and telescoping sums for advanced series problems. * Learn foundational algebraic inequalities, including the Arithmetic Mean-Geometric Mean (AM-GM) inequality and its applications. * Configure step-by-step strategies for solving pattern recognition and summation problems efficiently. The material is structured starting with basic terminology and definitions, moving through detailed derivations of summation formulas, and finishing with dedicated modules on advanced series manipulation and fundamental inequalities. This course is designed for absolute beginners or students needing a rigorous refresher in high-school level algebra. No prior specialized knowledge is required. Start building your mathematical foundation today.