# Book:J.A. Green/Sequences and Series

## J.A. Green: Sequences and Series

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

ISBN 7100 4344 9.

### 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