# Chapter 5. Infinite Sequences and Series

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch5

Copyright © 2003 John Wiley & Sons, Inc.

Book Title

## Advanced Calculus with Applications in Statistics, Second Edition

Additional Information

#### How to Cite

Khuri, A. I. (2002) Infinite Sequences and Series, in Advanced Calculus with Applications in Statistics, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471394882.ch5

#### Publication History

- Published Online: 26 MAR 2003
- Published Print: 1 NOV 2002

#### Book Series:

#### Book Series Editors:

- David J. Balding,
- Peter Bloomfield,
- Noel A. C. Cressie,
- Nicholas I. Fisher,
- Iain M. Johnstone,
- J. B. Kadane,
- Louise M. Ryan,
- David W. Scott,
- Adrian F. M. Smith and
- Jozef L. Teugels

#### ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884

- Summary
- Chapter

### Keywords:

- absolute convergence;
- alternating series;
- bounded sequence;
- Cauchy criterion;
- Cauchy's product;
- comparison test;
- conditional convergence;
- divergence;
- Gauss's test;
- moments of a distribution;
- monotone sequence;
- power series;
- Raabe's test;
- radius of convergence;
- ratio test;
- rearrangement of series;
- root test;
- uniform convergence;
- Weierstrass's M-test

### Summary

Chapter 5 covers infinite sequences and series of real numbers, including tests of convergence for series of positive terms. It also covers rearrangement and multiplication of series, sequences and series of functions, uniform convergence of sequences and series, power series, and sequences and series of matrices. The last section covers applications in statistics, including a discussion concerning moment and cumulant generating functions, the weak and strong laws of large numbers, and ridge regression.