Limit Comparison Test

This calculus 2 video tutorial provides a basic introduction into the limit comparison test. It explains how to determine if two series will either both converge or diverge by taking the limit of the ratio of the two sequences to see if it equals a positive finite number. Examples and practice problems include series that can be simplified and compared to a p-series or a geometric series.

Integral Test For Divergence:

Remainder Estimate - Integral Test:

P-Series:

Direct Comparison Test:

Limit Comparison Test:

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Alternating Series Test:

Alternate Series Estimation Theorem:

Absolute & Conditional Convergence:

The Ratio Test:

The Root Test:

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Series Tests - Practice Problems:

Taylor & Maclaurin Polynomials:

Taylor's Remainder Theorem:

Power Series - Interval Convergence:

Power Series - Derivatives & Integrals:

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Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

[Adrian_Gutier]

Bro you are really making the difference in this world. Thank you for helping us.. Tomorrow's Engineers and other professionals would always keep you in ours minds, because you just made it easy for us to closed the open gaps in the concept.

[reganmian]

I crushed calculus 2, thanks to this channel, and now I'm in graduate school enjoying these as a quick reviews of the tedious mechanics of calculus

[pfeliciano]

I recommend watching the direct test first and then the limit one because it’s easier to understand

[yesufhassen]

Whenever I have confusion, I search your video and understand what going on. Thanks bro!

[laila]

0:22-1:22 For anyone who is confused about why the last question is divergent when the limit=1, this explains it. This is an important rule to remember, it is simply a proof. The limit doesn't determine the answer. It just proves that the answer found for one series (bn in this case) is going to be the same for the other (an).

[kelvinmasasire]

You may actually be the reason i pass my engineering maths test this coming Monday. Really helpful explanation video. I had not yet come across such clear and concise explanation. Thank you

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[coloredpandas]

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[JManTheOddball]

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[georgesadler]

Professor Organic Chemistry Tutor, thank you for another great video/lecture on the Limit Comparison Test in Calculus Two. This is a very important test in determining convergence and divergence of a series. Learning different tests for convergence/divergence can be a challenge for all students in Calculus. Thís is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[kelvincheng]

I have my calculus 2 final in 1 hour. Sir, you just cleared my doubts about the limit comparison test. Thank you for so much.

[collinpowell]

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[Vincent-KN]

In the second example, you have to calculate the first term of the series, n=0, therefore obtaining the series that starts at n=1. After that, you just have do exactly what JG did about the harmonic series. When you see that the new series is divergent and the limit test gives you 1, you can unify the first term to the series that starts at n=1, and then obtain the one the you had a the beginning.

[pfeliciano]

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[sahilkatta]

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[beachwave]

taking 4 summer classes. have my second calc exam next Wednesday. if I pass this exam, actually no. if I pass this semester in calc 2, I owe it all to you. calc 2 in 10 weeks is a big beast but im currently kicking its ass

[zxynb]

how do we know if we should use the limit comparison test or the direct comparison test?

[marcosjohnsonnoya]

Thanks my guy, I usually watch khan, but this filled a lot of gaps in my understanding that i couldn't get with khan.