| 作者简介： Daniel Donald Bonar did his Ph.D. work in complex analysis at Ohio State University where he graduated in 1968. In 1965 he joined the faculty of Denison University in Granville, OH where he has been teaching mathematics, statistics, and computer science. In 1995 he was appointed to the newly created George R. Stibitz Distinguished Professorship in Mathematics and Computer Science. He is the author of a book entitled "On Annular Functions", and is co-author on several research papers. He has published joint work with the internationally acclaimed Hungarian mathematician Paul Erdos. |
| 1 Introduction to Infinite Series 1.1 Definitions 1.2 Special Series 1.3 Intuition and Infinity 1.4 Basic Convergence Tests 1.5 General Series 2 More Sophisticated Techniques 2.1 The Work of Cauchy 2.2 Kummer's Results 2.3 The Tests of Raabe and Gauss 2.4 Logarithmic Scales 2.5 Tests of Abel Appendix: Proofs of Bertrand's Tests 3 The Harmonic Series and Related Results 3.1 Divergence Proofs 3.2 Rate of Growth 3.3 The Alternating Harmonic Series 3.4 Selective Sums 3.5 Unexpected Appearances 4 Intriguing Results 4.1 Gems 5 Series and the Putnam Competition 5.1 The Problems 5.2 The Solutions 6 Final Diversions 6.1 Puzzles 6.2 Visuals 6.3 Fallacious Proofs 6.4 Fallacies, Flaws and Flimflam 6.5 Answers to Puzzles Appendix A: 101 True or False Questions Appendix B: Harmonic Series Article Appendix C: References Books on Infinite Series Books with Excellent Material on Infinite Series Sources for Excellent Problems Related to Infinite Series Pleasurable Reading Journal Articles Index About the Authors |
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