Direct Comparison Test - Calculus 2

This calculus 2 video tutorial provides a basic introduction into the direct comparison test. If the big series converges, then the smaller series must also converge. Likewise, if the small series diverges, the big series must diverge as well. That's the basic idea of the direct comparison test. Typically, you need to compare the series you're analyzing with a simpler p-series or geometric series to tell if the original series will converge or diverge.
Integral Test For Divergence:
• Calculus 2 - Integral ...
Remainder Estimate - Integral Test:
• Remainder Estimate For...
P-Series:
• P-series
Direct Comparison Test:
• Direct Comparison Test...
Limit Comparison Test:
• Limit Comparison Test
_________________________________
Alternating Series Test:
• Alternating Series Test
Alternate Series Estimation Theorem:
• Alternate Series Estim...
Absolute & Conditional Convergence:
• Absolute Convergence, ...
The Ratio Test:
• Ratio Test
The Root Test:
• Root Test
__________________________________
Series Tests - Practice Problems:
• Calculus 2 - Geometric...
Taylor & Maclaurin Polynomials:
• Taylor Polynomials & M...
Taylor's Remainder Theorem:
• Taylor's Remainder The...
Power Series - Interval Convergence:
• Power Series - Finding...
Power Series - Derivatives & Integrals:
• Power Series - Differe...
___________________________________
Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

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[@gemslk]

Isn't 1/n convergent

[@audiomac]

@@gemslk 1/n is convergent, but its series is not. Look up p-series to look up more on the topic.

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[@rmdir]

An analogy.
You are driving home in your car with a friend. The car is low on gas, the low gas light comes on.
Your friend lives a few miles before your house, on the way, less distance.
If you make it home (converge) of course so did your friend.
But if your friend makes it home, that doesn't mean you won't run out of gas on the way to your house (diverge).
Same situation here.

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[@Silenwrld]

10:34

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[@pfeliciano4062]

The problem at 11:50ish is true guys because remember we have been given a restriction if n is greater than or equal to 3. So if you were to plug in 3 you can actually see that 1/n is smaller.
Also keep in mind that you need to simplify for the second to last problem n/n^2 becomes 1/n

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Thanks a lot sir 👍. I got cleared the concept of direct comparison test . I wasn't knowing it so clearly .

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Remember if An=< Bn it will converge unless An goes to negative infinity

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Question: "IN THIS VIDEO," if a sub n is inconclusive, do we leave the answer like that? Do we have to solve further to find if a sub n ("an") is divergent t or convergent?

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[@clutchmadness]

@11:44, I don't understand how he arrived at 1/n. Can someone please explain? All in all, it's still a great video :)

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because the numerator becomes insignificant compared to the denominatoe?

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[@rodneygolpe3614]

In the problem 1/4+ n^1/3 , can't I use 1/n for comparison? 1/n < 1/4+n^1/3. Since 1/n diverges, then 1/4+n^1/3 diverges.
Correct me if I'm wrong

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on the Direct Comparison Test in Calculus Two. This topic in Calculus Two can be problematic, however students must know the different tests and how to apply them in different cases. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.

[@alialogaily882]

Hey ive got a question for the second example, would it be possible to just re - index the series to then perform the p -test (so we make n = 6) (n = 1 + 5)? or only viable at n = 1?

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[@aineshbalaga1216]

can you use the integral test on the last one?

[@jae9932]

11:50 could you use the integral series test for this?

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[@user-ch6xl1zc6k]

I don't quite understand how it works in the case of a decreasing series. If bn is larger than an, but both are decreasing then how does bn converging tell us that an also does

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[@alchemyofwonders]

dircet comparision test of (n+2^n)/(n^2*2^n) how to do it ??

[@johnperez3454]

At 12:10 why is it allowed to do n >= 3 I thought all Bn terms had to be bigger than An terms. Is it because they are only 2 terms that dont follow that which doesnt affect the whole series because only 2 terms affecting a series of infinite terms is very small relative to it.