Telescoping Series

This calculus 2 video tutorial provides a basic introduction into the telescoping series. It explains how to determine the divergence or convergence of the telescoping series. It also explains how to use the telescoping series to find the sum of the infinite series by taking the limit as n goes to infinity of the partial sum formula. This tutorial contains examples and practice problems with factoring and partial fraction decomposition with the telescoping series.

Improper Integrals:

Converging & Diverging Sequences:

Monotonic & Bounded Sequences:

Absolute Value Theorem - Sequences:

Squeeze Theorem - Sequences:

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Geometric Series & Sequences:

Introduction to Series - Convergence:

Divergence Test For Series:

Harmonic Series:

Telescoping Series:

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Integral Test For Divergence:

Remainder Estimate - Integral Test:

P-Series:

Direct Comparison Test:

Limit Comparison Test:

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Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

[farhanalam]

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[kidusbahiru]

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[msong]

I've said this before and I'll say it again. You are a lifesaver. What you explained in 20 minutes, my professor could not in 2 hours.

[fullreinhard]

Thank you for this. We went over telescoping series for practically 5 minutes in class out of 2 weeks and its probably going to be on the exam, yer a lifesaver.

[anthonymason]

I know you get this a lot, but good job. You really are great at explaining things concisely. Which helps those of us just learning the information for the first time. Cheers.

[Shosk]

you are a legend.... i just dont have a knack for sequences and series but you just made my day and thank you all the way from South Africa

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[crneymar]

series are literally going to be the death of me. the rest of calc 2 has been so easy up until now

[georgesadler]

Professor Organic Chemistry Tutor, thank you for an awesome explanation of the Telescoping Series Test in Calculus Two. Pattern recognition and problem solving increase my full understanding of the Telescoping Series Test. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

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[marin]

My logic on the last problem is that once it starts repeating I counted at how many terms it repeated. This number was 3 [ ]'s. So then I always do 1- that many terms, and this is how I determine the exact amount of an-x terms that I would need. I also observed that it will always involve the first numbers in the bracket for the first listing and the last numbers in the brackets for the an-x listing. I know my explanation sounds confusing but hopefully, someone finds it helpful.

[jamalaldin]

for the last problem, how did you know to start with an-5?

[mr.prince]

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[rabiekarouia]

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[aheedatif]

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[karlgrant]

How do you know what number to do for An-#? Don't get why we did An-1 on one problem but An-2 on another

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