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This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.

Tabla de contenidos provista por Syndetics

• Preface
• 1 Introduction to infinite series
• 2 More sophisticated techniques
• 3 The harmonic series and related results
• 4 Intriguing results
• 5 Infinite series and the Putnam competition
• 6 Final diversions
• Appendix A 101 true or false questions
• Appendix B Harmonic series article
• Appendix C References

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CHOICE Review

Students in typical modern calculus courses learn techniques, little recipes for working exercises, more than they develop technique--the integrated mathematical virtuosity that enables genuine problem solving. A century ago a calculus book such as G. H. Hardy's A Course of Pure Mathematics (10th ed., 1952) could go far beyond introducing tools and really teach the tricks of the trade; the title alone would cause an allergic reaction in marketing today. So particular topics get especially short shrift--case in point, the closed-form summation of infinite series--because mastery requires the acquisition of a knack and because of the widespread false perception that software somehow renders real skill dispensable, at least for the practically inclined. Thus this book by Bonar (Denison Univ.) and Khoury (Ohio State Univ.) works like a nutritional supplement that merely replaces what overprocessing has sadly robbed from the diet. A copy in the library will aid enlightened and conscientious instructors. No student with a hand in contest mathematics can afford to miss it. As a classroom resource, it will have no purpose once this era of bloated and vacuous calculus texts ends, but that day lies far in the future. ^BSumming Up: Recommended. General readers, lower-division undergraduates, faculty, professionals. D. V. Feldman University of New Hampshire