# Science:Infinite Series Module/Units/Unit 1/1.3 Infinite Series

## What This Lesson Covers

In this lesson we introduce

- the definition of an infinite series
- the definition of convergence of an infinite series
- a test for determining if a given infinite series converges based on its partial sums
- the definition of the geometric series
- a formula for the sum of a convergent geometric series

## Learning Outcomes

After reading this lesson and after you have completed a sufficient number of the recommended problems, students should be able to

- determine if a given series is a geometric series
- determine if a geometric series converges
- calculate the sum of a geometric series

Simply reading the content in this lesson will not be sufficient. Students will need to get out your pencil and paper and complete problems in order to prepare themselves for assessments related to this lesson.

## Topics

It is recommended that students progress through this lessons in the given order, as the sections build upon each other.

- Introduction to Infinite Series
- Convergence of Infinite Series
- The Geometric Series
- A Geometric Series Example
- Converting an Infinite Decimal Expansion Into a Rational Number
- Finding the Sum of an Infinite Series
- A Geometric Series Problem with Shifting Indices
- Koch Snowflake Example
- Introduction to Infinite Series Videos
- Final Thoughts on Infinite Series

## Additional Resources for This Lesson

- Additional Example 1: Geometric Series with Shifting
- Additional Example 2: Converting an Infinite Decimal Expansion to a Ratio of two Integers
- Additional Example 3: Finding the Sum of an Infinite Series
- Videos for the Introduction to Infinite Series Lesson