The+Integral+Test

﻿The I ntegral Test for Convergence

The integral test is a convergence test that is best to use when you are given a sum that is easy to integrate.

An early form of the [integral] test of convergence was developed in India by Madhava in the 14th century, and by his followers at the Kerala School. In Europe, it was later developed by Maclaurin and Cauchy(who also is known for the nth root test) and is sometimes known as the Maclaurin–Cauchy test.(source: Wikipedia)

The integral test says that(taken from [|link]):

Let f(x) be a continuous positive function that is eventually decreasing and let f(n) = a subscript n 

converges if and only if



converges. Furthermore,

 diverges if and only if

 diverges.


 * Examples:**

Note that the result of the limit found in the integral test is the number that the sum converges to, unless said limit is infinity, in which case the series is divergent.




 * Try it yourself!**


 * [|Integral text explanation & worksheet]**
 * Do #1-6, 9-10, and 13-15 on page 7**


 * [|Solutions to problems listed above]**