Ratio Test

As a rule of thumb, if the series contains n's in the exponents or contains one or more n!'s, then the ratio test will be your best bet.

Still not quite getting the hang of it?The video to the left explains the test and does a couple of examples step-by-step.

The ratio test can prove to be especially useful when it is used on alternating series, because it eliminates the possibility of the series being conditionally convergent.

Here's the basics!

Ratio Test

Watch Part 2 of his video here.

The negative sign on the e disappeared because we are taking the absolute value.

Note:(n+1)! = (n+1)*n!ande^(n+2) = e^(n+1)*eRewriting this way helps with cancelling if you are having trouble seeing how the numerator simply became an e.

Here's an example worked out for you to see.