Limit Comparison Test

This calculus 2 video tutorial provides a basic introduction into the limit comparison test. It explains how to determine if two series will either both converge or diverge by taking the limit of the ratio of the two sequences to see if it equals a positive finite number. Examples and practice problems include series that can be simplified and compared to a p-series or a geometric series.
Integral Test For Divergence:
kzbin.info/www/bejne/nGq2e61qYrqUh7M
Remainder Estimate - Integral Test:
kzbin.info/www/bejne/rJK4Znd6mLmZkM0
P-Series:
kzbin.info/www/bejne/rmeVYqWqftyVlZY
Direct Comparison Test:
kzbin.info/www/bejne/pYvXcpqfndSea9U
Limit Comparison Test:
kzbin.info/www/bejne/gnPbioRmia-rj68
_________________________________
Alternating Series Test:
kzbin.info/www/bejne/eoOyYp6GiZmciZo
Alternate Series Estimation Theorem:
kzbin.info/www/bejne/fJy4o3Sdd990kNE
Absolute & Conditional Convergence:
kzbin.info/www/bejne/fIGuZ3-FZs6cjsU
The Ratio Test:
kzbin.info/www/bejne/oZzJen-PpdB9iZo
The Root Test:
kzbin.info/www/bejne/l5nJYZiOhNGfZ68
__________________________________
Series Tests - Practice Problems:
kzbin.info/www/bejne/ZorIgIFqpZWindk
Taylor & Maclaurin Polynomials:
kzbin.info/www/bejne/q6Ozequsg6eLfJI
Taylor's Remainder Theorem:
kzbin.info/www/bejne/ooqTfa2Ajbmam9E
Power Series - Interval Convergence:
kzbin.info/www/bejne/e3jRmmVjopqsrq8
Power Series - Derivatives & Integrals:
kzbin.info/www/bejne/pHWZmZSfaJesobM
___________________________________
Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
www.patreon.com/MathScienceTutor/collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/eoOyYp6GiZmciZo Final Exams and Video Playlists: www.video-tutor.net/

[@onwabadosini2962]

Think you made a mistake in the third one, isn't the limit as n approaches infinity of 1/3^n equal to zero ? Please confirm.

[@L_is_con]

They were talking about sum of 1/3/^n@@onwabadosini2962

[@user-qv1li5qn5u]

@@onwabadosini2962 indeed the limit as n approaches infinity of 1/3^n =0 but in the 3 problem we are limit comparing (1/3^n +5 * 3^n /1) = lim(3^n / 3^n + 5) and that equals 1

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[@pfeliciano4062]

I recommend watching the direct test first and then the limit one because it’s easier to understand

[@davidthomas5077]

100% true

[@avthecool129]

u are 100% correct

[@reganmian]

I crushed calculus 2, thanks to this channel, and now I'm in graduate school enjoying these as a quick reviews of the tedious mechanics of calculus

[@laila1901]

0:22-1:22 For anyone who is confused about why the last question is divergent when the limit=1, this explains it. This is an important rule to remember, it is simply a proof. The limit doesn't determine the answer. It just proves that the answer found for one series (bn in this case) is going to be the same for the other (an).

[@briannauquillas]

Thank you!!

[@justins7796]

thanks! couldn't have said it better

[@jaimeirigoyenlopez5884]

You mean the one before last?

[@yesufhassen7422]

Whenever I have confusion, I search your video and understand what going on. Thanks bro!

[@kelvinmasasire6737]

You may actually be the reason i pass my engineering maths test this coming Monday. Really helpful explanation video. I had not yet come across such clear and concise explanation. Thank you

[@carmin.]

You are doing wonders for Engineers during quarantine 💖 Many universities are closed and it is challenging to navigate course work and keep up from home. You videos really make a difference :)

[@zxynb]

how do we know if we should use the limit comparison test or the direct comparison test?

[@bunny-bunny-bunny]

I love you, thanks for the videos. I wouldn't be passing calc 2 otherwise- your videos are well explained and concise!

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another great video/lecture on the Limit Comparison Test in Calculus Two. This is a very important test in determining convergence and divergence of a series. Learning different tests for convergence/divergence can be a challenge for all students in Calculus. Thís is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@JManTheOddball132]

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[@coloredpandas1993]

I have a test on this Monday and I plan to binge watch these videos and make a much needed A on this test!! Thank you sooo sooo much!!

[@blooberization]

fail

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You’re AMAZING you make everything so much easier i loved it! Thank you so much

[@pfeliciano4062]

Awesome video!!! I love the way you teach us like you have a God-given gift. God bless you you are a grade saver! I literally don’t even care that I don’t get the material in the class cuz In the end you are my real teacher always! ✍🏻❤️

[@FlamingFlareon]

Thanks! I was looking for how to solve one of these problems algebraically and what you did made perfect sense.

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[@michaelbanks1000]

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[@shaunt1309]

Thanks you so much for making these videos! They really help!

[@AngelSoft-ex4wd]

Amazing video, literally running through my math problems because of your extraordinary explanations! Thank you!

[@Vincent-KN]

In the second example, you have to calculate the first term of the series, n=0, therefore obtaining the series that starts at n=1. After that, you just have do exactly what JG did about the harmonic series. When you see that the new series is divergent and the limit test gives you 1, you can unify the first term to the series that starts at n=1, and then obtain the one the you had a the beginning.

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[@Ali_Pxll]

last problem can be solved using direct comparison test really appreciate your effort man, thanks.

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You are saving my university grades for Calc II. I love you!

[@kirbymia6209]

Thanks for the video! You are an awesome teacher!

[@juancarrillo6993]

When you plot the series, both converge to the cero. 1/n as n is greater and greater the sum is approaching to cero (0)

[@arianeparadis6439]

Thank you again for the 56th time for helping me understand and review my calculus, physics and organic chemistry. If I pass my semester I owe it to you.

[@Daniilope]

Did you pass the semester

[@arianeparadis6439]

@@Daniilope I did 😁 I almost didn't pass organic chemistry but I made it. This channel helped me pass Calculus 1, Calculus 2 and physics.

[@Daniilope]

@@arianeparadis6439 that’s so good to hear! Currently calculus is kicking my butt so hopefully this channel works it’s magic like it did on you 😭🙏

[@arianeparadis6439]

@@Daniilope Don't give up! Calculus can be difficult to understand. If you understand the reason behind using a certain formula or type of limit you'll find it easier to remember. It's a lot of practice. Wish you the best!

[@christinatimalsina5584]

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[@fatmacdacat]

Thanks again OCT. I can now sleep soundly in my bed knowing how to execute the LCT. You are the best.

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taking 4 summer classes. have my second calc exam next Wednesday. if I pass this exam, actually no. if I pass this semester in calc 2, I owe it all to you. calc 2 in 10 weeks is a big beast but im currently kicking its ass

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[@_kevin_wong_]

Got my final in 6 minutes and ofc this guy saves the day again haha

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Thank u sooo much sir for ur kindness and for helping us

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Thanks my guy, I usually watch khan, but this filled a lot of gaps in my understanding that i couldn't get with khan.

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You are awesome, sir. Keep it up!

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you sir have blessed me

[@luissanoja6096]

excelente video, muy practico para el aprendimiento rapido.

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[@alicesze1360]

Best teacher everrrrr

[@asadrking]

You are so helpful!

[@kelvincheng999]

I have my calculus 2 final in 1 hour. Sir, you just cleared my doubts about the limit comparison test. Thank you for so much.

[@iMusikkForeva]

I'm curious too...can't just leave us hanging dude

[@asadrking]

I guess you didn't learn the limit comparison test as well as you had hoped.

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How did you do?!?

[@kelvincheng999]

Well, I graduated college 2 months ago but I did pass the test. I remembered that I got an 87 on that final and now I work in tech. Success story 😂

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@@kelvincheng999 you give me hope, I have a calc 2 midterm tomorrow and hopefully will pass.

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WHAT KIND OF LEGEND ARE YOU

[@lordfarquaadreal9156]

2:33 we now finally know what Gunna and Future were talking about when they said they were pushing P, they were talking about Calc 2 Limit Comparasion test, p=3. They're ahead of the rap game so much man, Drake's out there sampling Alvin and the Chimpunks and they're out here sampling Limit Comparasion Tests and Differential Calculus. Kudos to them and OCT! 🤲🤲

[@AlbertoRivas13]

Excelent explanation sir

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if i can get through my physics program, i will be proud to say that youre basically my instructor 😊

[@blissnotes3477]

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[@davidfrancis285]

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[@kxvix8774]

you are a life saver 💌

[@warwick802]

for those who didnt understand the part in #2 where he removed the 5 in the limit, you can use L'Hopital on the limit which is ln3*3^n/ln3*3^n which cancels out to 1

[@camillewhite7861]

thank you!

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يسطا لو فهمتها ياريت تشرحهالي عليا اختبار بعد بكرا ده الانستا بتاعي . (_5stc) ولو ملقتهوش خد ده endl9

[@iigreenstarii]

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[@Alex-kd4vo]

Thank you for this video! Could you please do another video like this but working with e?? Most of my homework and practice quizzes have those types problems.

[@MyDavidrock]

just a heads up, you have the harmonic series at 5:49 going from 0 to inf.. but its undefined at zero

[@darcash1738]

Bravo, maestro

[@tomveer9885]

wouldn't the example at 8:17 be solvable through the direct comparison test?

[@ephemeronchimera]

So would the first example.

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[@namehere630]

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[@intkayne736]

Thank you

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Thank you 🙏🏻

[@mygoal3441]

The Organic Chemistry Tutor you are too much

[@mustafaalihussain340]

Thank you, but I think the summation in the series b_n should starts from 1 not from zero.

[@kevint681]

Youre the reason I'm passing with A's on exams in Calc 2

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imagine getting A's in calc 2..i wish.

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[@megsperry2925]

@@adansilva6851 good luck :, )

[@cloudyo_o2792]

carrying my degree rn

[@cenkocenk]

thank you

[@amirwagih4797]

ur a legend man!

[@leahbronstein9205]

what if you are using the limit comparison test for a series that isn't a rational expression (for examples, ln(sec(1/n)), how would we go about this problem?

[@MatthewAyoob]

You are amazing!!!

[@hermannebbinghaus3040]

Aww! I literally just had my test 3 hours ago! It’s okay tho, I still love you ♥️

[@tokamak4219]

Hope you scored high!

[@hannanbaig7888]

Why do you multiply the numerator and denominator with 1/n at 6:55?

[@PK-wr6kz]

Can anybody suggest where I can see more such examples as shown in this video using this specific technique ?

[@Christian-jm5jv]

Can anyone please explain the step at 6:55? When he multiplied the top and bottom by 1/n. Thanks!

[@bilinmezevren-291hzu]

if you understand that, can you please explain it to me?

[@sarahdonnelly5236]

@@bilinmezevren-291hzu He's basically multiplying it by one but in a different form. 1/n divided by 1/n is 1. The denominator of sqrt(1/n^2) actually simplifies to 1/n. The reason that he puts it under the square root though, is so he can multiply the radicands and just keep it under the square root.

[@unknowno_o8220]

If you watched the direct comparison test video he has, hes subtly nudging that test when he goes to prove b_n or an as either convergent or divergent.

[@wizben3135]

Thanks so much for everything

[@janem8664]

I'm just wondering, but isn't the last problem technically a Direct Comparison Test?

[@Zyngawf9]

@@mundheral-ahmadi8939 I was thinking the same thing. I think he's just taking it one step further.

[@santoshupretimadara]

thanks man a lot

[@SISKCERTWaJaVlogs]

4:47 not to mention 1/n^3 is bigger than a of n so DCT would work too

[@faichalayeva3677]

Thank you, sir.

[@uzumakikuroko9000]

FAIRA Fa Hey, @8:53, do you know how 1/3^n became (1/3)^n? Thanks

[@faichalayeva3677]

@@uzumakikuroko9000 yes because 1^2=1, 1^(2000)= 1 1 exponent anything is one. So you still have the same term 1/(3)^n I hope it helped.

[@uzumakikuroko9000]

FAIRA Fa yeah, that’s true. Thank you for your help, I was just kinda skeptical whether or not it is “legal” to go from 1/3^n to (1/3)^n. But your explanation made it clear, so thanks again☺️

[@syum1100]

How can you teach soooo efficiently

[@maryamanayat3350]

What is the some real-life application of comparison test?with examples.

[@muhammadusamajamil2685]

awesome may good give you what you want

[@realking4918]

I feel like I know this dude from around the way or something. Appreciate you bro!

[@bugfact9279]

Came for the profile picture, stayed for your playlists

[@realking4918]

@@bugfact9279 Lol appreciate that, just tryna be great

[@aboutdogzoffcial]

man thankyou!!

[@EternalClamness]

On example 2 I’m confused how you chose to divide by 1/n and sqrt of 1/n^2

[@AJ-rm7jp]

love you bro

[@mr.prince8701]

8:12 I'm a little confused. I thought bother series would converge since you got a finite sum with the limit comparison test of lim An/Bn, so if An or Bn diverge by themselves, then they bother diverge even after the LCT?

[@parkermell6990]

Ryan if you know Bn diverges and you do the test and get a finite number then An also diverges.

[@kylesteele5848]

6 months later I still wonder

[@saif0316]

Parker Mell and if you dont get a finite number?

[@Bamberosjose]

@@saif0316 If your answer is: > 0 , both series either converge or diverge =0 and Bn converges, then An also converges =Infinity and Bn diverges, then An also diverges

[@inuyasha11p]

@The Organic Chemistry Tutor how would u remove significance if the numerator has a trig such as sin(n)

[@inuyasha11p]

let's say u had summation from 0 to infinity (1+sin(n))/10^n. how would dis be solved using removal of insignificant stuff.

[@aleemprince3771]

so are you saying that if you get a finite number for the limit comparison then both are the same as the results you got from the direct comparison"?

[@omarsaadi9300]

n can not equal zero as your bn in the second example, in order to correct this i believe you should set both starting at n=1 and then add one to the n in the an.

[@JenniferRokks]

Wish I could like the video 100000x

[@moazelsawaf2000]

Thanks sir

[@samueldarenskiy6893]

so, for the limit comparison test you do not need to compare if the new series b_n is bigger or smaller than a_n?

[@josephgeorge2513]

What happens if you have a constant in both the numerator and denominator. 1. Which do you get rid off, if not both. 2.if the constant remains in either num or denim, can we disregard it when dividing an and bn?

[@brittniep9219]

Joseph George pull the constant out in front of the limit

[@brittniep9219]

Joseph George use limit laws

[@user-sf8wg4qf4t]

I don't understand the second example, where the first term is already divergent. Shouldn't the series start with n=1? In this case there was no problem but when we use 1/n^2 for comparison, (1/sqrt(n^4+1) on the left)we will get different answers(convergent if starting from n=1, divergent if the series starts with n=0) which is probably not the case in the series we want to test. What is wrong with this situation?

[@matthewgrove2770]

couldnt you use the direct comparison test for the last example? Because 1/(3^n + 5) is less than 1/3^n and 1/3^n converges, so by the direct comparison test, 1/(3^n + 5) would converge?

[@SISKCERTWaJaVlogs]

bingo

[@amish4448]

for the second example, why are you able to use 1/n when if sub n=0 , it is not finite which violates one of the constraints which says that the expression must be positive an finite for all values for n