About This Chapter
Sequences and Series for Calculus - Chapter Summary
Understanding how to evaluate series and sequences is an important foundation to exploring logarithmic and polynomial functions in calculus. In this chapter, we help you build that base through interesting videos filled with great instruction and entertaining graphics. Our instructors will give you loads of examples and practical applications as you explore sequences and series. Don't forget to take the self-assessments to make sure you're on track. The topics covered here include:
- Definitions of sequences and series
- Classifications of sequences
- Series notation and calculations
|What is a Mathematical Sequence?||Learn what a sequence is and what their importance is in mathematics.|
|How to Find and Classify an Arithmetic Sequence||Review the basics of describing sequences, in words and formulas.|
|Finding and Classifying Geometric Sequences||Explore sequence notation and exponential functions.|
|Summation Notation and Mathematical Series||Use sigma to describe sequences and series.|
|How to Calculate an Arithmetic Series||Learn how to quickly calculate the total number of items in a basic series using the summation equation discovered by Gauss.|
|How to Calculate a Geometric Series||See formula for solving geometric series.|
|Arithmetic and Geometric Series: Practice Problems||Explore classic sequence/series problems,|
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. 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.
5. 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.
6. 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!
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Other chapters within the AP Calculus AB & BC Textbook course
- Graphing and Functions
- Exponentials and Logarithms
- Exponents and Polynomials
- Applications of Derivatives
- Calculating Derivatives and Derivative Rules
- Differential Equations
- Area Under the Curve and Integrals
- Graphing Derivatives and L'Hopital's Rule
- Integration and Integration Techniques
- Integration Applications
- Rate of Change
- Geometry and Trigonometry
- Operating a Scientific Calculator