Real Infinite Series
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An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results.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 ...
An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results.
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.
Review quote:
'One chapter offers 107 concise, crisp, surprising results about infinite series. Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to problems of infinite series, and solutions ...' L'enseignement mathematique
Table of contents:
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.
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.
Review quote:
'One chapter offers 107 concise, crisp, surprising results about infinite series. Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to problems of infinite series, and solutions ...' L'enseignement mathematique
Table of contents:
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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