# Ch 26: Sequences and Series: Help and Review

### About This Chapter

## Summary

The sequences and series chapter of this College Algebra Help and Review course is the simplest way to master arithmetic, geometric and mathematical sequences and series. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of sequences and series.

## Who's it for?

Anyone who needs help learning or mastering college algebra material will benefit from taking this course. There is no faster or easier way to learn college algebra. Among those who would benefit are:

- Students who have fallen behind in understanding sequences and series
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about sequences and series
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the sequences and series chapter exam.

### Why it works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the sequences and series chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any sequences and series question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

### Students will review:

This chapter helps students review the concepts in a sequences and series unit of a standard college algebra course. Topics covered include:

- Mathematical sequences
- Finding and classifying arithmetic sequences
- Finding and classifying geometric sequences
- Calculating mathematical, geometric and arithmetic series

### 1. What is a Mathematical Sequence?

Math is often the most fun when it acts like a puzzle to be solved. The branch of math where this is the most true involves sequences. Get an introduction to the basics and important vocabulary, as well as learn where sequences appear in nature!

### 2. How to Find and Classify an Arithmetic Sequence

Arithmetic sequences are everywhere, and with a few tricks you learn here, you could end up looking like a psychic the next time you go to a movie or a football game!

### 3. Finding and Classifying Geometric Sequences

Want your YouTube video to get a lot of hits? Besides including a cute baby or an adorable cat, getting your video to have a big common ratio is the key. Learn what I'm talking about here!

### 4. Summation Notation and Mathematical Series

The capital Greek letter sigma might be most recognizable as a common symbol in a fraternity or sorority, but it's used for some pretty cool math tricks too. In this lesson, learn how to use sigma for things like determining how many seats are in Michigan Stadium.

### 5. How to Calculate an Arithmetic Series

In this lesson, you'll learn how to sum up any arithmetic sequence without having to add up each and every term. You'll never guess the circumstances that led to the discovery of this marvelous formula.

### 6. How to Calculate a Geometric Series

If you're not satisfied with knowing how many views your YouTube video will get any one day and need to know how many total views you're getting, geometric series are for you! Learn more in this lesson.

### 7. Arithmetic and Geometric Series: Practice Problems

There are many different types of problems concerning series and sequences - including some that are pretty abstract. From bouncing balls to adding up odd numbers, test your skills here with additional arithmetic and geometric series practice!

### 8. Arithmetic Series: Formula & Equation

After this lesson, you will be able to identify summation notation and interpret each of its parts when used for an arithmetic series. You will also be able to find the sum of an arithmetic series.

### 9. Harmonic Series in Math: Definition & Formula

The harmonic series provides one of the most important counter-intuitive examples in the study of mathematics. In the harmonic series, the numbers or terms get closer and closer to zero, while the series itself diverges.

### 10. Infinite Series: Applications, Formula & Examples

An infinite series, represented by the capital letter sigma, is the operation of adding an infinite number of terms together. This summation will either converge to a limit or diverge to infinity.

### 11. Maclaurin Series for ln(1+x): How-to & Steps

In this lesson, we show how to find the Maclaurin series for a particular function: ln(1 + x). In addition to the steps for finding this series, you will also learn how to determine its region of convergence.

### 12. Taylor Series for sin(x): How-to & Steps

In this lesson we show how to find the Taylor series for the sine function. Using examples, we look at the series evaluated about two different values of x.

### 13. Taylor Series for ln(1+x): How-to & Steps

In this lesson, we show how to find the Taylor series for ln(1+x). This is a series evaluated about a specific point so we also look at the interval of convergence about this point.

### 14. Representing the ln(1-x) Power Series: How-to & Steps

In this lesson, we find the power series for ln(1-x) by deriving a simpler series and then integrating it. This lesson includes how to find the interval of convergence.

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### Other Chapters

Other chapters within the College Algebra: Help and Review course

- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Exponents and Exponential Expressions
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Algebraic Expressions and Equations
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Functions: Help and Review
- Fractions
- Factoring
- Exponentials and Logarithms: Help and Review
- Probability Mechanics: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Basic Number Sense and Operations