# Science:Infinite Series Module/Units/Unit 1/1.1 Infinite Sequences

## What This Lesson Covers

In this lesson we introduce

• the definition of convergence of an infinite sequence
• various theorems on limits of infinite sequences, including
• the theorem relating between the limit of a function and a limit of a sequence
• the limit laws for infinite sequences
• the squeeze theorem for infinite sequences
• the theorem on the limit of the absolute value of a sequence

## Learning Outcomes

After reading this lesson and completing a sufficient number of problems, students should be able to

• determine whether an infinite sequence converges using the theorems presented in this lesson

Simply reading the content in this lesson will not be sufficient. Students will need to get out a 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.

1. Introduction to Infinite Sequences
2. Convergence of Infinite Sequences
3. Convergence of Infinite Sequences Example
4. Relationship to Limits of Functions
5. Limit Laws for Infinite Sequences
6. Limit Laws Example
7. Relationship to Sequences of Absolute Values
8. Example Relating Sequences of Absolute Values
9. Squeeze Theorem for Sequences
10. Squeeze Theorem Example
11. Example: rn
12. Videos on Infinite Sequences
13. Final Thoughts on Infinite Sequences