Ratio Test for Convergence of an Infinite Series

The Ratio Test stands as a fundamental tool in the analysis of infinite series convergence, offering a systematic approach to assess the behavior of divergent or convergent series. Widely employed in calculus and mathematical analysis, the Ratio Test scrutinizes the ratio of consecutive terms within a series to determine its convergence or divergence. By exploring the limiting behavior of this ratio, mathematicians gain insights into the series' convergence characteristics, paving the way for a more profound understanding of infinite mathematical structures. In this brief exploration, we will unravel the key principles and applications of the Ratio Test in the context of infinite series.