Радикальна ознака Коші як інструмент дослідження широкого класу задач

Abstract

This paper explores the Cauchy radical sign as one of the fundamental methods for determining the convergence of numerical and power series. The theoretical justification of the sign, its advantages compared to other convergence criteria, and the features of its application in mathematical analysis problems are considered. It is shown that the radical sign is an effective tool for studying series with power and exponential components. Examples of using the Cauchy sign for practical analysis of series convergence are given.