Lesson 6

1. Lesson 6

1.5. Explore

Mathematics 20-1 Module 1

Module 1: Sequences and Series

Explore

This image shows a silhouette of a couple against a background of a cloudy sky and a broken-line graph. The man is holding a glowing nest egg in his hand.

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The money you save towards your retirement years is often referred to as your nest egg. The nest egg is built up during your working years. The nest egg increases in size as a result of regular contributions to your investment and interest earnings.

In retirement, you can have your nest egg paid out to you in a series of regular payments, called an annuity. Depending on the amount of money in the nest egg and the size of the annuity, you could make your retirement savings last a very long time.

An annuity that continues forever is called a perpetuity. Do you see a way you could turn your retirement savings into a perpetuity?

In this lesson you will study infinite geometric series. You will extend your knowledge of geometric series to an infinite number of terms. You will learn how to identify those infinite geometric series with sums versus those without. You will derive formulas for evaluating an infinite geometric series. You will also solve problems involving these types of series.

You already saved Module 1 Glossary Terms in your course folder. In this lesson, you will define the following terms, and maybe others, in your copy of Module 1 Glossary Terms:

infinite geometric series
limit
convergent
divergent
annuity
perpetuity