Convergence & divergence of telescoping series  Sequence and Series
Convergence & divergence of telescoping series
In this lesson, we will learn about the convergence and divergence of telescoping series. There is no exact formula to see if the infinite series is a telescoping series, but it is very noticeable if you start to see terms cancel out. Most telescopic series problems involve using the partial fraction decomposition before expanding it and seeing terms cancel out, so make sure you know that very well before tackling these questions.
Basic concepts:
 Partial fraction decomposition
 Introduction to infinite series
Lessons
Notes:
There is no exact formula for a telescopic series.

1.
Convergence of Telescoping Series
Show that the following series are convergent and find its sum: