# Ch 43: Progressions, Series & Logarithms

### About This Chapter

## Progressions, Series & Logarithms - Chapter Summary

Top instructors take you on an engaging journey through the basics of progressions, series and logarithms in this chapter. Discover or strengthen your existing knowledge of topics that include the binomial theorem, infinite geometric series and the sum of squares and cubes. When finished, you will be able to:

- Differentiate between arithmetic, geometric and harmonic progressions
- Calculate an arithmetic and geometric series
- Use the formula to calculate the sum of an infinite geometric series
- Share the definition of the sum of squares and cubes
- Expand binomial expressions using the binomial theorem
- Recognize and work with logarithms

Lessons in this chapter are fun to review and easy to navigate, enabling you to quickly and effectively expand your understanding of progressions, series and logarithms. Choose any lessons to study, and visit them as often as needed. When ready, gauge your comprehension of their contents by taking accompanying multiple-choice quizzes. Any questions you have about specific lesson topics can be submitted to our experts.

### 1. 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.

### 2. 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.

### 3. Understand the Formula for Infinite Geometric Series

Watch this video lesson to learn how to calculate the sum of an infinite geometric series. Learn about the interesting thing that happens when your common ratio is less than one.

### 4. Sum of Squares & Cubes: Definition & Calculations

This lesson develops two important summation formulas that are used extensively in math and science. The formulas are used for computing the sum of the squares and the sum of the cubes of the first n whole numbers.

### 5. The Binomial Theorem: Defining Expressions

In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.

### 6. What is a Logarithm?

Logarithms can help you solve exponential functions. In this lesson, you will learn about how to work with and recognize logarithms, and how to use logarithm notation with an example problem about earthquakes!

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