P Series Test-Definition, Applications, and Examples

In the realm of mathematical analysis, determining whether a series converges or diverges is a fundamental question. The p-series test provides a valuable tool for investigating the behavior of a specific type of series known as the p-series. This article delves into the definition of the p-series, explores its properties, and provides a comprehensive understanding of its convergence or divergence.Definition of P Series TestThe p-series test is a method used to determine the convergence or divergence of a specific type of series called the p-series. A p-series is defined as the sum of the terms (1/nᵖ) for n ranging from 1 to infinity. Mathematically, it can be represented as:∑(1/nᵖ)In this representation, the symbol “∑” denotes the summation notation, “n” is the index variable that ranges from 1 to infinity, and “p” is a positive constant.The p-series test focuses on the value of the exponent “p” to assess the behavior of the series. The test establishes the following criteria:Converge...