### Introduction

In this Section we develop the ground work for later Sections on infinite series and on power series. We begin with simple sequences of numbers and with finite series of numbers. We introduce the summation notation for the description of series. Finally, we consider arithmetic and geometric series and obtain expressions for the sum of $n$ terms of both types of series.

#### Prerequisites

- understand and be able to use the basic rules of algebra
- be able to find limits of algebraic expressions

#### Learning Outcomes

- check if a sequence of numbers is convergent
- use the summation notation to specify series
- recognise arithmetic and geometric series and find their sums

#### Contents

1 Introduction2 Arithmetic and geometric progressions

3 Series

3.1 The summation notation

4 Summing series

4.1 The arithmetic series

4.2 The geometric series