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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc503870 |
| Date | 08 1900 |
| Creators | Abbott, Catherine Ann |
| Contributors | Lewis, Paul Weldon, Dawson, David Fleming |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 65 leaves: ill., Text |
| Rights | Public, Abbott, Catherine Ann, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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