1. Lesson 6

Mathematics 20-1 Module 1

Module 1: Sequences and Series

 

Lesson 6: Infinite Geometric Series

 
Focus

 

This shows three illustrations in a bucket: a cruise ship at night, a couple skydiving, and a portrait of three generations of women in a family.

Boat: iStockphoto/Thinkstock, Skydivers: Photodisc/Thinkstock, Family: liquidlibrary/Thinkstock

Do you have a list of goals you dream of accomplishing one day, perhaps when you retire? Some people refer to these goals as a bucket list. To others, they are just a list of goals. Either way, your dreams will need to be financed.

 

Visiting exotic destinations or embarking on a once-in-a-lifetime adventure costs money. Maybe your idea of a satisfying retirement is to stay close to home and indulge in a hobby or volunteer in your community. Either way, you will still need a steady income to maintain your daily expenses.

 

All working Canadians contribute to the Canada Pension Plan, which pays Canadians a monthly pension. Many Canadians also invest additional income in retirement savings plans. Upon retirement, Canadians draw on their pension, savings, and investments to provide a steady source of income. Ideally, this income will allow them to live comfortably and enjoy items on their bucket lists!

 

In this lesson you will investigate infinite geometric series. You will see that it is possible to predict the sum of an infinite number of terms. You will also learn how you can apply infinite geometric series to calculate the value of annuities paid over an indefinite period. By doing this, you can make informed decisions to secure your financial future.

 

Outcomes
 

At the end of this lesson you will be able to

  • generalize, using inductive reasoning, a rule for determining the sum of an infinite geometric series

  • explain why a geometric series is convergent or divergent

  • solve a problem that involves an infinite geometric series
Lesson Questions
 

In this lesson you will investigate the following questions:

  • When is it possible to add an infinite number of terms?

  • How are infinite sums used in finance?
Assessment

 

Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 6 Assignment (Download the Lesson 6 Assignment and save it in your course folder now.)

  • course folder submissions from Try This and Share activities

  • additions to Module 1 Glossary Terms and Formula Sheet

  • work under Project Connection