Exercises of Numerical Series E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

In this book exercises are carried out regarding the following mathematical topics: numerical series convergence criteria Initial theoretical hints are also presented to make the performance of the exercises understood

Leseprobe

Simone Malacrida

Exercises of Numerical Series

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Exercises of Numerical Series”

INTRODUCTION

THEORY OF NUMERICAL SERIES

EXERCISES

“Exercises of Numerical Series”

“Exercises of Numerical Series”

SIMONE MALACRIDA

In this book exercises are carried out regarding the following mathematical topics:

numerical series

convergence criteria

Initial theoretical hints are also presented to make the performance of the exercises understood

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – THEORY OF NUMERICAL SERIES

Definitions

Operations

Notable series

Convergence criteria

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 1 4

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 21

Exercise 22

Exercise 23

Exercise 24

Exercise 25

Exercise 26

Exercise 27

Exercise 28

Exercise 29

Exercise 30

Exercise 31

Exercise 32

INTRODUCTION

INTRODUCTION

In this exercise book, some examples of calculations relating to numerical series and the respective convergence criteria are carried out.

Understanding the fundamentals of numerical series is fundamental for tackling the subsequent steps, such as the one represented by the series of functions or by their series expansions.

Furthermore, numerical series are well suited for a mathematical generalization of practical and applicative problems, already known since ancient times.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

Although no background in mathematical analysis is necessary to understand numerical series (and therefore their study can also be undertaken at the upper secondary level), the different concepts of convergence presuppose, at least, a topological notion that is only an introduction to analysis can support.

I

THEORY OF NUMERICAL SERIES

THEORY OF NUMERICAL SERIES

Definitions

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A series is the sum of the elements of a sequence and is a generalization of the addition operation, extended to the case of infinitely many terms.

The series symbol is called summation and is indicated as follows:

while the extreme variations of the sum are indicated at the bottom and top:

If the upper index is finite we speak of a sequence of partial sums, if it is infinite we speak of a true and proper series.

The series is said to be convergent if there is a finite number which equals the sum of all its elements.

This value is called the sum of the series.

If this limit is infinite, the series is divergent, if instead the limit does not exist, the series is called oscillating .

Convergent and divergent series are called regular .

A necessary condition of convergence of a series is that the infinite nth element is zero.

A numerical series is a series whose elements are numbers.