--- title: Sequences & Series description: Sequences are ordered lists of numbers, while series are the sums of those sequences. Learners will understand arithmetic and geometric progressions, convergence tests, and summation notation, enabling them to analyze infinite processes and approximate functions. category: mathematics subcategory: algebra difficulty: beginner, intermediate, advanced url: /subject/sequences-and-series --- # Sequences & Series Sequences are ordered lists of numbers, while series are the sums of those sequences. Learners will understand arithmetic and geometric progressions, convergence tests, and summation notation, enabling them to analyze infinite processes and approximate functions. ## Available Resources 5 Courses • 4 Websites ## Websites ### 1. Calculus II: Series & Sequences **Author:** Paul Dawkins Chapter of Paul Dawkins's free Calculus II notes covering sequences, infinite series, partial sums, the integral, comparison, alternating, ratio and root tests, absolute convergence, power series and Taylor series, with worked examples. Learners can decide convergence and represent functions as power series. **Difficulty:** Intermediate | **Price:** Free **Link:** https://tutorial.math.lamar.edu/classes/calcii/seriesintro.aspx **Tags:** sequences, infinite-series, convergence-tests, power-series, taylor-series ### 2. Art of Problem Solving Wiki - Sequences A reference entry from the Art of Problem Solving wiki defining sequences, recursion, and common families, with linked competition problems. Useful for olympiad and contest preparation once the basic definitions are already familiar. **Difficulty:** Beginner | **Price:** Free **Link:** https://artofproblemsolving.com/wiki/index.php/Sequences **Tags:** sequences, recursion, competition-math, problem-solving, aops ### 3. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 4. mathsisfun.com MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathsisfun.com **Tags:** websites, mathematics-statistics, algebra ## Courses ### 1. Sequences and Series Brilliant's interactive course built around problem sets covering arithmetic and geometric progressions, recursion, and summation techniques. Learners practise pattern-finding and closed-form summation by solving rather than by reading proofs. **Difficulty:** Intermediate | **Price:** Paid **Link:** https://brilliant.org/courses/sequences-and-series/ **Tags:** sequences, series, arithmetic-sequences, geometric-sequences, problem-solving ### 2. Arithmetic and Geometric Sequences Khan Academy's Algebra 1 unit on sequences, with videos and exercises on recursive and explicit formulas. After working through it a student can extend a sequence, write its formula, and evaluate any term. **Difficulty:** Intermediate | **Price:** Free **Link:** https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences **Tags:** sequences, arithmetic-sequences, geometric-sequences, algebra, recursive-formulas ### 3. Introducción al cálculo **Author:** Jaume Pujol, Mercè Villanueva Spanish-language course from the Universitat Autònoma de Barcelona that reviews numbers and functions, polynomial, exponential, logarithmic and trigonometric functions, then introduces differentiation, integration and complex numbers. Prepares students for a first-semester university calculus course in science or engineering. **Difficulty:** Beginner | **Language:** English | **Duration:** 6-8 horas de trabajo por módulo | **Price:** Free **Link:** https://www.coursera.org/learn/introduccion-al-calculo **Tags:** precalculus, functions, trigonometry, differentiation, integration, spanish-language ### 4. Introduction to Complex Analysis **Author:** Petra Bonfert-Taylor Wesleyan University course on complex analysis covering complex numbers, analytic functions, conformal mappings, Möbius transformations, contour integration, Cauchy's theorem, power and Laurent series, and residues. Learners finish able to evaluate contour integrals and analyze complex-differentiable functions. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/complex-analysis **Tags:** complex-analysis, analytic-functions, conformal-mapping, contour-integration, residue-theorem ### 5. Algebra: Elementary to Advanced - Polynomials and Roots **Author:** Joseph W. Cutrone Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/polynomials-roots **Tags:** polynomials, factoring, exponents, radicals, algebra --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/sequences-and-series