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

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## J.A. Green:

## J.A. Green: *Sequences and Series*

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

- ISBN 7100 4344 9.

### Subject Matter

### 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*

- 1.

- 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*

- 1.

- 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*

- 1.

- Answers to Exercises

- Index

## 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 $4$