Root Test

This calculus 2 video tutorial provides a basic introduction into the root test. If the limit of the nth root of the absolute value of the sequence as n goes to infinity is less than 1, the series converges. If it's greater than 1, the series diverges. If it's equal to 1, the root test is inconclusive.

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:

[Watercolors]

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[lavina]

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[abamanass]

Am having an exam tomorrow and these videos on convergence test are really getting me into the zone.Thanks

[MyMinecrafter]

Yo man, just wanted to thank you for all your videos. You helped me a lot with physics and organic chemistry and i passed :)

[PrimeOTA]

6:24 how did u manage to take that 2 out of the absolute value just like that, we have a 1 over n as a power :)

[michaellu]

7:10 you made an error taking out 1/2 when it should've been 1/2^(1/n) but nevertheless the answer is the same and thank you for your help

[nikkiblair]

I once heard a famous mathematician say that math is a language. So turn it into a language and use math in terms of words. And you have this incredible ability of turning it into words that I can easily understand and comprehend. When I read my math books, I get lost in the crazy mumbo jumbo. I literally will look up your videos before reading my textbook. Thanks for helping me earn my BA in Mathematics.

[bigdaddie]

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[georgesadler]

Professor Organic Chemistry Tutor, thank you for another incredible video/lecture on the Root Test in Calculus Two. Once again, the Root Test is not difficult, however students could have some problems with the basic algebra and using La Hospital's rules in Calculus. Professor Organic Chemistry Tutor, at the 6:26 minute mark in the video, you pulled out 1/2 instead of 1 divided by 2 raised to the one divided by n. The final solution, however, is one hundred percent correct. Please correct this small error in the video.

[richardfrederick]

In the fourth example a factor of 1/2 was pulled out of the absolute value signs. This was an invalid operation, since the entire expression within the absolute value signs, including the 2 in the denominator, must be raised to the 1/n power.

[jakep]

Hello to all the people watching this video two hours before the test.

[MuhammadSalman-zgfv]

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[originalrider]

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[aimanali]

Thanks for the video, am in an exam now. Helped me cheat!!!

[HA-fxzf]

6:22
i think you cannot do that. taking out the 2 of the absolute value to the power of 1/n !

[Brisun]

At 5:03 if you do the comparison test you get that it diverges by the p test since 1/n^2 is greater than 1

[iamlove]

is it possible to take out the 2 at 6:29 i see it is inside the nth root ??

[luckyhubchannel]

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[lucid]

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[mr.]

In that last example, it's good that break 3 to the (n+2) into 2 parts, but since 3 squared is a constant that is independent of n, just bring it out to the front of the summation. This'll save time (and reduce your chance of making a silly mistake since you're not doing any unnecessary calculations).