A Second Look at the Second Ratio Test

Abstract

This article examines a class of series convergence tests, known as the mth ratio tests, that were introduced by Sayel A. Ali in 2008. We pay particular attention to the case where m = 2. We also consider the relationship between these tests and other convergence tests, namely Raabe’s test and Jamet’s test, that are based on an implicit comparison with a p-series.

Keywords:

• MSC: Primary 40A05
• Secondary 26A12

Acknowledgments

The authors are grateful to Warren P. Johnson and to the anonymous reviewers for their helpful comments and suggestions.

ORCID

Christopher N. B. Hammond http://orcid.org/0000-0001-7327-0544

Additional information

Notes on contributors

Christopher N. B. Hammond

Christopher N. B. Hammond received his B.A. from the University of the South in Sewanee, Tennessee and his Ph.D. from the University of Virginia. He has taught mathematics at Connecticut College since 2003. His primary research interests relate to function-theoretic operator theory.

Department of Mathematics and Statistics, Connecticut College, New London, CT 06320

[email protected]

Edward Omey

Edward Omey received his Ph.D. from the University of Leuven (Belgium), where he has taught mathematics and statistics as part of the economics faculty. His research interests relate to asymptotic theory in probability theory and analysis.

Research Centre for Mathematics, Education, Econometrics and Statistics, KU Leuven, Campus Brussels, Warmoesberg 26, 1000 Brussels, Belgium

[email protected]