# 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.

- Introduction to Infinite Sequences
- Convergence of Infinite Sequences
- Convergence of Infinite Sequences Example
- Relationship to Limits of Functions
- Limit Laws for Infinite Sequences
- Limit Laws Example
- Relationship to Sequences of Absolute Values
- Example Relating Sequences of Absolute Values
- Squeeze Theorem for Sequences
- Squeeze Theorem Example
- Example: r
^{n} - Videos on Infinite Sequences
- Final Thoughts on Infinite Sequences