Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-20T16:29:24.103Z Has data issue: false hasContentIssue false
  • English
  • Français

A Generalized Comparison Test

Published online by Cambridge University Press:  20 November 2018

Elgin Johnston
Elgin Johnston*
Affiliation:
Department of Mathematics, Iowa State University Ames, Iowa 50011
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let ∑ cj and ∑dj be, respectively, convergent and divergent series of positive terms and let ∑ aj be a third series of positive terms. It is well known, [1, pg. 275] that ∑ aj converges if lim sup(aj/cj)<+∞, but diverges if liminf(aj/dj)>0. In this note we prove a generalized version of this comparison test that relies not on term-by-term comparison of the series, but on the relative densities of the terms of the series.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 485 - 487
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Knopp, K., Theory and Application of Infinite Series, Hafner Publishing Company, New York, 1947.Google Scholar