Nth Term Test for Divergence of an Infinite Series

The Nth Term Test for Divergence is a fundamental concept in the study of infinite series, providing a crucial tool for determining the convergence or divergence of a series based on the behavior of its individual terms. This test, rooted in the principles of mathematical analysis, examines the behavior of the sequence formed by the terms of the series as \( n \) approaches infinity. By assessing whether the terms tend to zero or diverge, the Nth Term Test offers valuable insights into the convergence properties of infinite series, laying the groundwork for further exploration of their mathematical properties and applications.