4.1 Introduction

What is a geometric series? Take a quantity, and repeatedly subject it to a constant proportionate change.

Example - Inflation: assume a 3% yearly inflation rate. How many years until a nominal dollar has only half its current purchasing power?

Start with one dollar, at the end of year 1 you would need $1.03 to purchase the equivalent of $1.00 in the original year.

At the end of year 2, you need another 3% more, that is $1.03 \times 1.03 =$1.0609.

At the end of year 3, you need another 3% more, that is $1.0609 \times 1.03 =$1.0927.

How many years until you need $2.00?

This is a geometric series, because you start with a quantity, $1.00, and repeatedly subject it to a constant proportionate change, multiply by 1.03.