Limit Comparison Test (KristaKingMath)

► My Sequences & Series course: www.kristakingmath.com/sequen...
Limit Comparison Test calculus problem example.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@redhedgehogx4076]

She melts my heart when she says "hey everyone!!" at the beginning haha I am still learning from her even if some videos are a decade old. She's the best

[@mehularora1813]

The quality of these videos is sooo good! It really surprises me when I read 8 years ago, 10 years ago...

[@kristakingmath]

You are so sweet, Hedgehog, I'm so glad you're enjoying the videos!! :D

[@kristakingmath]

Thank you so much, Mehul!! :D

[@michaelwilcox3197]

I just watched a couple other videos on this by much more popular people and still had no idea but after watching your video once I completely understand. Your gifted at teaching, don't ever give it up! You alone have probably saved thousands of kids from failing haha thank you and keep it up!

[@kristakingmath]

Aw thanks! I'm so glad I could help! :)

[@XPTPCREWX]

Theres a lot of videos on youtube that try to explain the LCT but I think this is the best one, mainly because you are thorough and spend enough time through the reasoning. Thanks for your insight!

[@kristakingmath]

Thanks!

[@sterlingbubolz3896]

this is the greatest thing ive ever seen on youtube. you actually just summed up a week of my calc class. thank you soooo much!!

[@segould]

This was very helpful! I'm taking a summer Calc 2 course right now. I have a final in two days, and I'm doing a lot of work with series right now. I could not really understand how to use the Limit Comparison Test until you said that you choose Bn based on what terms have the greatest effect on the magnitude of An. Thanks so much! I'm sure that I'll be watching your other series videos as well!

[@caitlinswim131]

Series is the first subject in calculus, or even math that I've ever struggled with. Your videos on all the different tests have helped me so much!! Thank you!

[@kristakingmath]

You're welcome! I'm so glad they've helped. :) Sequences and series are some of the hardest calc topics for most people!

[@vn6938]

Why can't my professor be this helpful? Thank you very much!

[@kristakingmath]

I'm glad I can help!

[@juhairahadji-daud5869]

I really like the way you teach. Out of all KZbin tutorials I've been checking out, you're the best one so far. U always manage to answer my questions in mind. Thank you so much! You're a great help with my Mathematics subjects. I do hope you'll keep on helping us 😊

[@kristakingmath]

I appreciate that, JUHAIRA! I'm so glad my videos have been able to help so far! :D

[@juhairahadji-daud5869]

Wow! You noticed my comment@@kristakingmath 💕

[@kristakingmath]

you're welcome, i'm so glad you liked it!!! :D

[@kristakingmath]

yes! you can find the table here: integralcalc(dot)com/convergence-tests/. :)

[@0diepus]

Thanks for quick reply; taking last test tomorrow. This will come in handy. Have a great day!

[@kristakingmath]

Glad you liked it!

[@talesofadam8]

Thanks again for illuminating a complex idea with such clarity! Of all the series tests, this is the one I've had the hardest time understanding, particularly how to choose b_n.

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@talesofadam8]

I don't suppose you could give me some insight on: sum[4n^2 / (6n^3 + 2n +5)^(1/2)] ? Can you do a limit comparison against... sum[4n^2 / (6n^3)^(1/2)]? Is there a better way to evaluate this series?

[@talesofadam8]

Nevermind, I think a simple divergence test of sum[4x^2 / (6x^3 + 2x +5)^(1/2)] is enough because its limit as x goes to infinity isn't zero.

[@kristakingmath]

You're awesome! Thanks for the comment. :)

[@kristakingmath]

You're welcome! I sincerely hope that my videos have been helpful. :) Please let me know if you ever have questions about the Academy; I would love to have you as a member! :)

[@kristakingmath]

Thanks!

[@PtotheMtotheJ]

Very helpful video, thanks!

[@djelite07]

Great example! Love your video's :)

[@lifeasagem]

Praise you!

[@kristakingmath]

You too, and GOOD LUCK on your test!! :D

[@wilerjrxd]

Awesome explanation! :D

[@westermjean2723]

Thank you Krista King!

[@kristakingmath]

You're welcome, Westerm! :)

[@heejonghan3052]

You are the amazing itself!

[@iwillrocktheplace]

Hey Ms.King can we use the tables you told us about in the videos while doing the comparison test for improper integrals ?

[@adeline9452]

you are the best!!..thank you so much, my best grade in calc is because of you..thank youuuuu..

[@kristakingmath]

Lei Adlyn I'm so glad I can help!

[@fredfan86]

Thanks, extremely helpful. Think I now have a fighting chance in my calc exam!!

[@tirthachakrabarti5912]

good one really..I've got a question..if L i.e. the final limit turns out to be positive infinity, what to do? it says L has to be greater than zero i.e. positive but is that only finite positive? or also positive infinite is allowed?

[@sharonsolana]

You're the best!

[@5cents100]

How do you know when to use the Limit Comparison test and when to just use the Comparison test? Or are they the same thing?

[@jasminsahota5803]

I really appreciate these explanations. They have helped me understand the process, step by step. So thank-you :)

[@kristakingmath]

+Jasmin Sahota You're welcome, I'm so glad the videos are helping!

[@barskorkmaz8323]

+Jasmin Sahota I agree with you she is awesome but she didn't mention two things The limit could also be equal to 0 or infinity .

[@hg2.]

Yes, she's the best math teacher on KZbin. All other KZbin instructors should watch Krista to learn how it's done.

[@WacoBeautyQueen]

What if your series is something like (2n^2-1)/(3n^2+4). What series do you compare this to? Because I know when you have 2n^2/3n^2 the powers cancel each other out so how do we fulfill all the rules of LCT?

[@mahmoodobada9191]

what if bn, or an less than or equal zero what series test i have to use

[@0diepus]

Sup, sup, Ms. K!!!!! thanks for helping me through Calc 1, 2. Noticed vids keep getting tech advanced as time goes on; from white board on floor to full-on computer use. Anyways, you mention in this vid a convergence table. Can't find on your site. If possible, please direct me to it? Gracias!!!

[@rvbCabooservb]

Better videos then patrickJMT but I love learning from both of you guys.

[@kristakingmath]

Good luck! :)

[@jordiburguesmiro2096]

How is it that an diverges because of bn, but the limit between both series exists? Thank you so much.

[@satadhi]

how can Bn be divergent ! if a telescoping series .Somebody please help !

[@superoxidedismutase5757]

why do we divide an/bn?

[@kristakingmath]

you're welcome!! :D

[@godfreypeter7547]

great work.

[@kristakingmath]

Thanks! :)

[@godfreypeter7547]

you are welcome :)

[@CubanSauce]

1/n diverges? Why? As n gets bigger doesnt it approach 0?

[@edsepulveda23]

Aw man you are awesome!!! Thank you so much! I think I'm in love haha jp

[@hg2.]

Sorry if this is a dumb question, but isn't this Converging instead of Diverging?

[@free2beme485]

Why is the series divergent when L= to a positive tangible number (10)? How would the student now that 1/n is harmonic?

[@Mericali916]

When you get to the point of learning the Limit Comparison Test, it is inferred that you have already been exposed to the harmonic series, geometric series, telescoping series, etc.

[@laimino]

Why don't we have to consider coefficient 10 ?

[@kristakingmath]

Hey! :) I have the table on my website here: integralcalc(dot)com/convergence-tests/. Hope that helps! :)

[@Olivia-gc2wk]

hi there, can you please help me to solve one math problem? please...

[@faisalaseeri4545]

THANKS A LOT MISS...SO INTERESTED WITH YOUR WAY OF TEACHING NOW I CAN FEEL MORE CONFIDENCE WITH CAL.C HOPE TO JOIN YOUR ACADMY KUWAIT ENGINEERING FACULTY.

[@lindsaychewe8583]

Thanks integralCALC!!

[@kristakingmath]

You're welcome!! :D

[@tsi4ya]

very good....but kinda like what everybody else does on here...this is easy problem that can be found in the book. Great explanation though.

[@thelegendaryone4566]

could we have still solved that problem with just the comparison test rather than the limit comparison test?

[@matthewyoungsoonam]

thanks. Couldn't figure out why 1/n was divergent. Guess its just a given

[@4rthgearindustries408]

+Matthew Nam Its divergent because of the p-series rule goes as, 1/(N^p) where if P is less than or equal to 1, it is divergent, and convergent if p>1

[@user-tm1ix7xi1n]

what if is less than 0? does that mean we cannot use comparison test?

[@kristakingmath]

Correct, you'd have to find a different test to use. :)

[@user-tm1ix7xi1n]

Krista King Thank You.

[@burakayan1429]

I apreciete so much , I am thankful to you :) I will watch all of your videos :D thank you a lot :D

[@kristakingmath]

You're so welcome! I'm glad you like the videos. :)

[@burakayan1429]

:D thanks for replying. I have calculus exam this friday. :D it will be about series and sequences. thanks to you again I'm studying :D

[@kristakingmath]

burak ayan Good luck!

[@iwillrocktheplace]

Thank you very much ma'am *raise my hat*

[@kopanomoss5752]

SMASH THE LIKE BUTTON

[@sharikgorilla176]

beautiful AND a nerd? she's perfect :)

[@sulemanamohammed2099]

Jesus Haploid Christ! Thank You!

[@rfonsec2281]

Smart and beautiful?? sorcery....

[@kristakingmath]

you're welcome!! :D