Foundations of Sequences and Series

Sequences and series are fundamental building blocks of higher mathematics, essential for understanding calculus, statistics, and financial modeling. If you struggle to identify patterns or calculate infinite sums, this course provides the clear, written guidance you need. By the end of this course, you will possess a strong conceptual and practical understanding of how sequences and series work. You will be able to confidently define, analyze, and manipulate arithmetic and geometric progressions, determine convergence, and use summation notation to solve complex mathematical problems. What you'll learn: * Learn the definitions and notation for sequences, series, and summation, starting with basic pattern recognition. * Master the formulas for calculating the nth term and the sum of terms in Arithmetic Progressions (AP) and Geometric Progressions (GP). * Understand the relationship between sequences, limits, and convergence, including tests for divergence and convergence of infinite series. * Apply knowledge of series to solve real-world problems involving compound interest, growth rates, and recurrence relations. * Practice manipulating special series, including harmonic series and basic telescopic sums, using written step-by-step examples. This course begins with terminology and foundational concepts before moving into detailed analysis of AP and GP. We then explore the behavior of infinite series and introduce practical applications through worked examples and written exercises. This course is designed for absolute beginners or anyone needing a thorough review of mathematical sequences and series. No prior advanced mathematical knowledge is required, only basic algebra skills. Start building your foundational mathematical toolkit today.