Learn how to use the integral test to check the convergence of infinite series of monotonic terms. See the statement, proof, applications and examples of the test, as well as related topics and references. · In this section we will discuss using the Integral Test to determine if an infinite series converges or diverges. The Integral Test can be used on a infinite series provided the terms of the series are positive and decreasing. A proof of the Integral Test is also given. Learn how to use the integral test to determine whether a series of positive terms converges or diverges. See examples, error estimation, and applications to harmonic and telescoping series. Luckily, several tests exist that allow us to determine convergence or divergence for many types of series. In this section, we discuss two of these tests: the divergence test and the integral test. · What is the Integral Test? The Integral Test is a test used in calculus to assess the convergence or divergence of an infinite series given in terms of the comparison with an improper integral. We show how an integral can be used to prove that this series converges. · Integral test relates series to an improper integral and is systematic with regard to finding convergence of series, especially when dealing with nice functions.
