Telescoping Series - Calculus 2

A special type of series you may encounter is what is known as a telescoping series. A telescoping series is a series whose terms collapse, or "telescope." In other words, we would say that many of the terms in the series cancel out, leaving us with only a couple terms to work with that actually determine the sum of the series.

Once a series has been identified as a telescoping series, determining its convergence becomes a fairly simple process. All we need to do is take a look at the nth partial sum, which is easily found due to the cancelling terms, and take the limit as n approaches infinity. 

Telescoping series can take many forms, including a form that can be hard to recognize at first glance. Sometimes using partial fraction decomposition for a series that includes a rational expression can reveal a telescoping series that was initially not apparent. We will take a look at this type of series and more in this new lesson for Calculus 2. So with that, let's get right to it!

In this lesson, you will learn:

• What a telescoping series is and how to identify one
• How to find the nth partial sum of a telescoping series
• How to determine the sum and convergence of a telescoping series using the nth partial sum.

I hope you find this video to be helpful!

-Josh