On the convergence of some alternating series

TL;DR

This paper investigates the convergence properties of a specific class of alternating series, including the series involving sine functions, providing new insights into their convergence behavior.

Contribution

It establishes the convergence of certain alternating series, notably including the series with sine functions, expanding understanding of convergence criteria.

Findings

Proved convergence of the series involving |sin n|/n

Identified conditions for convergence of alternating series

Analyzed the convergence sets of the studied series

Abstract

We study the convergence sets of a class of alternating series. Among other things, our results establish the convergence of the series $\sum_n (-1)^n|\sin n|/n$.