Mathematics Series On The Definition Of The Sum Of A Divergent Series

Author : Louis Lazarus Silverman
Publisher : Wentworth Press
ISBN 13 : 9780530086712
Total Pages : 106 pages
Book Rating : 4.19/5 ( download)

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Download or read book Mathematics Series on the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by Wentworth Press. This book was released on 2019-03-05 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Louis Lazarus Silverman
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.84/5 ( download)

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Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by . This book was released on 1913 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Louis Lazarus Silverman
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.91/5 ( download)

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Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by . This book was released on 1991 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Louis Lazarus Silverman
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781534890336
Total Pages : 102 pages
Book Rating : 4.35/5 ( download)

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Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by Createspace Independent Publishing Platform. This book was released on 2016-06-24 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents. § 1. Introduction § 2. Historical Resumé § 3. Averageable Sequences § 4. Product Definitions § 5. On Certain Possible Definitions Of Summability § 6. Definitions Of Evaluability § 7. Applications § 8. Tests For Cesaro-Summability § 9. Theorems On Limits §10. Conclusion * * * * * An excerpt from: § 2. Historical Resumé. The earliest interest in divergent series centers about the series 1 - 1 + 1 - 1 + ... If we assume that this series has a generalized sum s, then the series, obtained by dropping the first term, - 1 + 1 - 1 + 1... must, by the third fundamental requirement of page 2, also have a generalized sum which is obviously -s. We have then, s - 1 = -s or s = 1/2. Thus, if the series is to have any value at all, that value must be 1/2. And this is precisely the value which Leibniz was led to attach to the series, by different considerations. The sum of n terms of the series is 0 or 1 according as n is even or odd; and since this sum is just as often equal to 1 as it is to 0, its probable value is the arithmetic mean, 1/2. This same value was later attached to the series by Euler, in a more satisfactory, though not entirely rigorous manner. "Let us say that the sum of any infinite series is the finite expression, by the expansion of which the series is generated. In this sense, the sum of the infinite series 1 - x + x2 - x3... will be 1/(1 + x), because the series arises from the expansion of the fraction, whatever number is put in place of x." In particular, 1/2 = 1 - 1 + 1 - 1 + ... It is true, as has already been intimated, that none of the methods given above, to prove that the series should have the value 1/2, is satisfactory from a theoretical point of view. But objections have been raised to the result for practical reasons also....

Author : Louis Lazarus Silverman
Publisher :
ISBN 13 : 9781332768400
Total Pages : 116 pages
Book Rating : 4.07/5 ( download)

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Download or read book On the Definition of the Sum of a Divergent Series (Classic Reprint) written by Louis Lazarus Silverman and published by . This book was released on 2016-06-26 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the Definition of the Sum of a Divergent Series This paper was accepted as a dissertation by the Graduate Faculty Of the University Of Missouri in May, 1910, in partial fulfillment Of the require ments for the degree of Doctor Of Philosophy. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Godfrey Harold Hardy
Publisher : American Mathematical Soc.
ISBN 13 : 0821826492
Total Pages : 418 pages
Book Rating : 4.92/5 ( download)

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Download or read book Divergent Series written by Godfrey Harold Hardy and published by American Mathematical Soc.. This book was released on 2000 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface by J. E. Littlewood: "All [Hardy's] books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as well he might), and also that he looked forward to the task with enthusiasm. He had actually given lectures on the subject at intervals ever since his return to Cambridge in 1931, and he had at one time or another lectured on everything in the book except Chapter XIII [TheEuler-MacLaurin sum formula] ... [I]n the early years of the century the subject [Divergent Series], while in no way mystical or unrigorous, was regarded as sensational, and about the present title, now colourless, there hung an aroma of paradox and audacity."

Author : Charles Napoleon Moore
Publisher : American Mathematical Soc.
ISBN 13 : 0821846205
Total Pages : 114 pages
Book Rating : 4.09/5 ( download)

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Download or read book Summable Series and Convergence Factors written by Charles Napoleon Moore and published by American Mathematical Soc.. This book was released on 1938-12-31 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fairly early in the development of the theory of summability of divergent series, the concept of convergence factors was recognized as of fundamental importance in the subject. One of the pioneers in this field was C. N. Moore, the author of the book under review.... Moore classifies convergence factors into two types. In type I he places the factors which have only the property that they preserve convergence for a convergent series or produce convergence for a summable series. In type II he places the factors which not only maintain or produce convergence but have the additional property that they may be used to obtain the sum or generalized sum of the series. This book gives a generalized systematic treatment of the theory of convergence factors of both types, for simply infinite series and for multiple series, convergent and summable.... --Bulletin of the American Mathematical Society

Author : Glenn James
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.04/5 ( download)

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Download or read book Some Theorems on the Summation of Divergent Series written by Glenn James and published by . This book was released on 1917 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Matthew Boelkins
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781724458322
Total Pages : 560 pages
Book Rating : 4.29/5 ( download)

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Download or read book Active Calculus 2018 written by Matthew Boelkins and published by Createspace Independent Publishing Platform. This book was released on 2018-08-13 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

Author : CK-12 Foundation
Publisher : CK-12 Foundation
ISBN 13 : 1935983016
Total Pages : 603 pages
Book Rating : 4.19/5 ( download)

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Download or read book CK-12 Calculus written by CK-12 Foundation and published by CK-12 Foundation. This book was released on 2010-08-15 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.