Real Infinite Series by Daniel D. Bonar & Michael J. Khoury
This is a great resource of concepts and challenging problems that is useful for teaching and exploring infinite series at any level, in calculus, in analysis, or in preparation for the Putnam Examination. -David Bressoud, DeWitt Wallace Professor, Macalester College
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. Real Infinite Series presents the theory of real infinite series, including 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. Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to 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 (what Martin Gardner calls "look-see" diagrams), 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 devoted entirely or partially to infinite series.