Calculus 2 - Geometric Series, P-Series, Ratio Test, Root Test, Alternating Series, Integral Test
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- Опубликовано: 25 авг 2024
- This calculus 2 video provides a basic review into the convergence and divergence of a series. It contains plenty of examples and practice problems.
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-tuto...
Full-Length Videos and Worksheets:
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bro Imma have a maths test in 2 hours.. prof made all these incredibly convoluted.. I absolutely love the straightforward manner you built up this video. it is incredible that some people can sum up months of curriculum in 45 minutes and everything is clear, all seems easy and meaningful in contrast to endless lessons in uncomfortable chairs
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This is more like 1.5 weeks or so
howd you do?
Tbf tho actually learning the content vs memorizing the formulas are completely different. As a review tool, this is great but if you get asked a single out-of-the-box question that requires deep knowledge of the topic then just knowing a bunch of formulas isn't gonna give you the intuition to actually unpack any of this. I'm self-studying for BC and I find it helps a lot to watch these vids in tandem with another explanatory resource like Pauls Online or Khan Academy, which usually have intuitive explanations or proofs of each concept.
@@lambda5949 but it means nothing to me whether I memorize the formula or understand the formula, I just need a pass in order to continue my university study which is nothing about maths. It is just silly that my school make maths compulsory even for the history major.
@@dhuka4969 Oh yeah, in that case, this vid makes sense, didn't think universities required that kinda thing so I was assuming this vid was tailored for high schoolers.
1. Divergence Test: 0:21
2. Geometric Series Test: 0:58
3. P-Series Test: 1:51
4. Telescoping Series: 2:33
5. Integral Test: 5:01
6. Ratio Test: 6:12
7. Root Test: 7:14
8. Direct Comparison Test: 8:12
9. Limit Comparison Test: 8:59
10. Alternating Series Test: 10:28
11. Absolute Convergence AND Conditional Convergence: 11:26
12. Practice Problems: 12:41
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You explained 43 minutes, that's already like 3 weeks of calculus II all in 1 video! Thank you so much man!
We covered this topic within half an hour in our university🥲
@@nipuniherath1451 you covered 11 topics in half an hour??? u need a new university bro. that makes no sense. maybe 30min-1hr for each topic but not 30 min for all 11 lol.
@@Max-cu6bw Yeah we did all of these with sequences in one lecture
@@nipuniherath1451 30 minutes??? This is like 20% of all the content for calc 2
@@benjaminwhitehead4050 Over here at UT it's the same case lol they treat calc 2 as a weed-out class
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For the example at 35:58, could you also use the direct comparison test to show that the series is convergent?
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this series has helped me a lot with my examns, however the part where you are calculating de limit of certain things can be easier by just taking the coefficient of the unkown X with the highest exponential
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my hands are partially frozen and Im typing fast so forgive my grammar mistakes
16:02 geometric series
17:59 alternating series
22:04 telescoping series - partial fractions
29:26
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Kindly bring up more challenging examples to solve for us cos our lecturers aren't having mercy on us in our exams
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Is there a version of this video somewhere with difficult versions of these problems? These are far simpler than the ones I'm given
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I think the problem at 37:31, we can use direct comparison test instead of limit comparison test since the bn is larger than an already
19:25 lim n-> inf = 0, he said passes divergent test. I thought he just discussed that a series will diverge if the lim -> inf =/ 0. Yet, his example here claims it approaching 0 passes the divergent test? I am confused
edit: It's late. I see my error. "pass the divergence test" does not mean we want the series to specifically diverge. In an alternating series we WANT the lim -> inf = 0 so it *passes* the divergence test i.e. we can continue to prove the convergence of a series continung with the alternating series test by checking the next term is less than or equal to the previous term.
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5 hours......
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