ON STATISTICALLY CONVERGENCE IN REAL SERIES

In this study, the concept of statistical convergence in real number series is examined. Definitions, theorems, and specific examples related to statistical convergence of series are given. The statistical convergence of the real number series, which has been studied very little, is introduced by using the natural density function. Taking advantage of this relationship, new features are examined. Theorems written on this subject are included. The grouping and the rearrangement of the terms of statistical convergent series are examined. Concepts known for Cauchy convergence, such as the Cauchy criterion and the general term test, are considered for statistical convergence. Original theorems are written on this subject, and new examples are found. Furthermore, the statistical convergence of the series is examined using tests such as the Abel and Dirichlet tests. These tests are developed, and some examples are included. Lastly, the Leibniz test and the Mertens test used in the Cauchy product series were developed for statistical convergence.