Integral Test for Convergence of an Infinite Series

The Integral Test is a powerful tool in the realm of calculus used to determine the convergence or divergence of an infinite series by relating it to an improper integral. By establishing a connection between the series and the integral of a continuous function, the Integral Test provides a straightforward method for assessing convergence. This method is particularly useful when dealing with series whose terms are positive, decreasing, and continuous functions of a variable. Through analysis of the integral, mathematicians can effectively ascertain the behavior of the corresponding series, facilitating deeper understanding and application within various mathematical contexts.