A new test for convergence of positive series

TL;DR

This paper introduces a novel convergence test for positive series, extending Margaret Martin's classical test, offering a new tool for analyzing series behavior.

Contribution

It presents a new convergence test for positive series that generalizes and extends the classical test by Margaret Martin.

Findings

Provides a new criterion for convergence of positive series

Extends the classical test by Margaret Martin

Offers a practical tool for series analysis

Abstract

The paper provides a new test of convergence and divergence of positive series. In particular, it extends the known test by Margaret Martin [%\emph{Bull. Amer. Math. Soc.} \textbf{47} (6), 452--457 (1941)]. \emph{Bull. Amer. Math. Soc.} \textbf{47}, 452--457 (1941)].