Real infinite series By Daniel D. Bonar, Michael J. Khoury Jr.
2006 | 271 Pages | ISBN: 0883857456 | DJVU | 4 MB
This is an excellent book. The prose is very readable and there are numerous illustrative examples to clarify the main points. Chapter 1 defines infinite series, discusses intuition and infinity, and covers the basic convergence tests. Chapter 2 covers the work of Cauchy and discusses more involved tests of convergence such as Kummer's results, the tests of Raabe and Gauss, and the tests of Abel. Chapter 3 examines the harmonic series. Chapter 4 covers a number of interesting results involving infinite series. Chapter 5 presents 101 problems involving infinite series from the Putnam Mathematical Competition. Answers to all problems are provided. Chapter 6 presents a plethora of puzzles, proofs without words, fallacious proofs, and fallacies, flaws, and flimflam. Answers to the puzzles are given. Two appendices present 101 True or False questions on infinite series with answers and a brief article on harmonic series. References, both books and journals, are also given. A brief but thorough index concludes the book. This book would serve very well as a resource for high school and college calculus teachers. Undergraduate mathematics majors with an interest in infinite series would find it appealing. Finally, readers like myself who majored in mathematics but pursued other careers would enjoy using it to refresh their knowledge of infinite series.(they may need to review a little calculus). The authors have produced a gem of a book and anyone who has a passion for mathematics will enjoy reading this volume. Chapters 1 and 6 are especially readable, informative, and enjoyable. Chapter 6 is just plain fun! Get your hands on a copy of this book as it will provide hours of fascinating reading and problem solving.
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