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Convergence of Infinite Series

The purpose of this paper is to examine certain questions concerning infinite series. The first chapter introduces several basic definitions and theorems from calculus. In particular, this chapter contains the proofs for various convergence tests for series of real numbers. The second chapter deals primarily with the equivalence of absolute convergence, unconditional convergence, bounded multiplier convergence, and c0 multiplier convergence for series of real numbers. Also included in this chapter is a proof that an unconditionally convergent series may be rearranged so that it converges to any real number desired. The third chapter contains a proof of the Silverman-Toeplitz Theorem together with several applications.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc503870
Date08 1900
CreatorsAbbott, Catherine Ann
ContributorsLewis, Paul Weldon, Dawson, David Fleming
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 65 leaves: ill., Text
RightsPublic, Abbott, Catherine Ann, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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