Integral Test

Things to Remember:*To create f(x), you can almost always replace all the 'n's with 'x's.*f(x) must be continuous, positive, and decreasing in order to use the integral test.*If you get a finite value as a solution to the integral, it does NOT mean the series converges to that value; it ONLY means that the series converges in general.

Integral Test

Here it is in formal terms.It's not as scary as it looks! (If you like improper integrals).

Here is the logic flow for the Integral Test.

The video to the right shows another example of the Integral Test in action. In both videos, he shows you how to use the first derivative test to prove that functions are decreasing. Check with your professor...you may be able to just plug in the first few values for n and show that the terms are decreasing that (much faster) way!!

As he points out in the above video, there are often easier, faster tests that can be used to test these series. But the more tests you have in your toolkit, the better off you will be!