1. Home
  2. >Calculus
  3. >Sequence and Series
Help

Convergence & divergence of telescoping series

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. Telescoping Series Overview:
?
Examples
Lessons
  1. Convergence of Telescoping Series
    Show that the following series are convergent and find its sum:
    1. ∑n=1∞4n2+7n+12\sum_{n=1}^{\infty}\frac{4}{n^2+7n+12}
    2. ∑n=1∞1n2+4n+3\sum_{n=1}^{\infty}\frac{1}{n^2+4n+3}
    3. ∑n=1∞14n2−1\sum_{n=1}^{\infty}\frac{1}{4n^2-1}
  2. Divergence of Telescoping Series with different pattern
    Show that the series ∑n=1∞(−1)n \sum_{n=1}^{\infty}(-1)^n is a diverging telescoping series.
    Topic Notes
    ?
    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.
    There is no exact formula for a telescopic series.
    Basic Concepts
    ?