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Chapter 4

# Series

## 4.1 Introduction

### 4.1.1 Definition

In general a series sn is defined as a sum of a given number of terms ai such that

${s}_{n}={a}_{\text{1}}+{a}_{\text{2}}+...{a}_{n}=\sum _{i=1}^{n}{a}_{i}$

If n = , the series is said to be infinite series. If n is finite, it is said to be a finite series.

### 4.1.2 Convergence

In most practical applications, a series will have to be evaluated up to a given upper bound n. The higher this bound is chosen, the more exact the solution, but also the more time-consuming, complicated and computationally expensive the solution will become. Therefore a suitable trade-off for n must be found.

However, some of the more important series actually sum up to ...

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