Limit Comparison Test | Calculus 2 Lesson 26 - JK Math

[@sokhomteng]

You are saving my calculus 2. You make it simple enough to understand. You should have more subscribers.

[@Liamliam-d5p]

best calc teacher, I always recommend you, wish you had a physics series

[@JKMath]

Thank you! I appreciate the support :) Perhaps one day I could make an intro physics series, but there are so many math courses I want to cover first, as that is what I love teaching the most!

[@Velaldo-nw7ve]

You are very good in explaining. I'm not sure why you don't have more subscribers.

[@JKMath]

Thank you, I appreciate that! The channel is still relatively new, so it will take time to grow, but I'm committed to making more and more tutorial videos regardless. Feel free to spread the word and share these videos with others! :)

[@Eliem016]

The best to do it💯 I understood everything

[@AhmedAMayow]

Thanks please can you make other courses like differential equation, linear algebra and so on. Because your explanation is so clear 👌.

[@JKMath]

You're welcome! Glad you find my videos to be helpful :) I definitely plan to cover those math courses and others in the future, but it will be some time until I get around to them. Still need to finish my Calculus 3 series, which I will be getting back to very soon! I am just one person, so there is only so much I can do at once. Have to focus on one thing at a time!

[@haileykk1035]

Does the series we are testing on need to stay on the top of the fraction?

[@JKMath]

Yes, the series whose convergence/divergence you do not know and are trying to determine should be in the numerator of the fraction, while the comparison series or series that you do know converges/diverges will be in the denominator. In other words, for the LCT, the convergence/divergence of the series in the bottom will always imply the convergence/divergence of the series in the top. Hope this helps!

[@sid7066]

for the 1/4^n-5 problem, wouldnt direct comparison test be quicker? because the series we try to compare it to, is larger than the original series, so we know that b(n) > a(n) converges. Thoughts?

[@JKMath]

Yes you could also use the direct comparison test (DCT) for that series, for the reasons you mentioned. This particular video is for showcasing the limit comparison test and how to use it, so that's why I didn't consider using the DCT. The nice thing about series is that there is often multiple ways to get to the right answer. You can use one test, while someone else might use another test, and you can both be correct. Good thought!

[@luhohnel]

Wouldn’t the direct comparison test be fine here ?❤️

[@JKMath]

Depends on the series, but yes, there are going to be cases where both the Limit comparison test and direct comparison test work. This lesson video is specifically focused on how to use the limit comparison test, so of course I am going to use it for every example, despite that other tests could be used.

[@luhohnel]

@@JKMath thank you for the quick reply. Your videos really helped me in preparation for my test. I wish I found you sooner !