Microfluidics: Modeling, Mechanics and Mathematics

Chapter 4

Series

4.1 Introduction

4.1.1 Definition

In general a series s_n is defined as a sum of a given number of terms a_i such that

$s_n=a_{\text{1}}+a_{\text{2}}+...a_n={\displaystyle \sum _{i=1}^n{a}_i}$

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 ...