Book:J.A. Green/Sequences and Series

J.A. Green: Sequences and Series

Published $\text {1958}$, Routledge & Kegan Paul Ltd.

ISBN 7100 4344 9

Subject Matter

• Real Analysis

Contents

Preface

Chapter $1$. Sequences

1. Infinite sequences

2. Successive approximations

3. Graphical representation of a sequence

4. The limit of a sequence

5. Other types of sequence

6. Rules for calculating limits

7. Some dangerous expressions

8. Subsequences

9. Monotone sequences and bounded sequences

10. The functions $x^n$, $n^s$ and $n^s x^n$

11. Solution of equations by iteration

Exercises

Chapter $2$. Infinite series

1. Finite series

2. Infinite series

3. Convergent and divergent series

4. Some examples of infinite series

5. Some rules for convergent series

6. A test for divergence

7. The comparison test

8. The ratio test

9. The integral test

10. Series with positive and negative terms. Leibniz's test

11. Absolute convergence

12. Power series

13. Multiplication of series

14. Notes on the use of the convergence tests

Exercises

Chapter 3. Further techniques and results

1. Numerical calculation of the sum of a series

2. Estimating the remainder of a power series

3. Integration of power series

4. Differentiation of power series

5. Cauchy's convergence principle

6. Dirichlet's convergence test

Exercises

Answers to Exercises

Index

Next

Cited by

• 1960: Walter Ledermann: Complex Numbers

Source work progress

• 1958: J.A. Green: Sequences and Series ... (previous) ... (next): Chapter $1$: Sequences: $1$. Infinite Sequences: Example $4$