Limit Comparison Test

[@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

[@TitoAlhamad]

@@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

[@Adrian_Gutier]

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[@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

[@pfeliciano4062]

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

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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

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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

[@sleverlight]

Last minute studying isn't gonna work. You should've studied earlier. I should take my own advice too. My test us tomorrow. So yay

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Organic chemistry is a life saver

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[@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?

[@SemNome-gl1cb]

I get so happy every time a see you made a video on a subject I need to study 🙏

[@JManTheOddball132]

You're the OG homie. Thank you once AGAIN for enlightening us peasants about another math concept. Keep rocking man!

[@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.

[@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!

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Man has been saving me the past 7 years🙏😭

[@AngelSoft-ex4wd]

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

[@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.

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

[@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! ✍🏻❤️

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I love you, never gonna stop loving you, youre getting me through calculus and into an engineering degree.

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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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Thank you so much for this, you don't know how much this helped me... all ur vids have basically taught me more than my teachers at school lol

[@ghadah3916]

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

[@6stringski373]

Dude thanks again. I was struggling with this, but thanks to you I’m back on track. 🐐

[@Ali_Pxll]

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

[@ruymorais3409]

Watching you from Brazil, you're the best

[@christinatimalsina5584]

You are the best professor I have ever seen . ❣

[@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! 🤲🤲

[@marcosjohnsonnoya417]

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

[@FlamingFlareon]

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

[@fatmacdacat]

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

[@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.

[@_kevin_wong_]

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

[@Alifaga]

WHAT KIND OF LEGEND ARE YOU

[@zxynb]

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

[@Cobenski4]

If one doesn’t work, then use the other

[@yvng_arsh]

@@Cobenski4 ty

[@BhajanandArti]

i just became your fan ....after watching "comparison tests videos".....what an explanation👌👌....love you Sir 🙏 👉love from India ✌️👌

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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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[@shaunt1309]

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

[@MariaCaro95]

Your videos are immensely helpful and have gotten be through Organic Chemistry and now Calculus II. I would have failed without you so thank you!

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

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@@adansilva6851 good luck :, )

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Hope you scored high!

[@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!

[@kirbymia6209]

Thanks for the video! You are an awesome teacher!

[@alicesze1360]

Best teacher everrrrr

[@MyDavidrock]

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

[@syum1100]

How can you teach soooo efficiently

[@sawairajamil1617]

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

[@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.

[@tomveer9885]

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

[@ephemeronchimera]

So would the first example.

[@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)

[@darcash1738]

Bravo, maestro

[@luissanoja6096]

excelente video, muy practico para el aprendimiento rapido.

[@iigreenstarii]

You are a life saver, Thank you !

[@moazosama]

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

[@iigreenstarii]

@@moazosama معلش والله مخدتش بالي من الريبلاي إلا دلوقتي سوري😂. أتمنى تكون أديت كويس.

[@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.

[@realking4918]

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[@realking4918]

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[@AlbertoRivas13]

Excelent explanation sir

[@zainabinam2636]

Thank you sooooo much

[@mustafaalihussain340]

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

[@MonsieurButter]

I'm still a bit confused. If the limit comparison test depends on the regular comparison test to tell if its convergent/divergent, what is the point of the limit comparison test? Isn't the limit comparison test just an unnecessary extra step?

[@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.

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carrying my degree rn

[@davidfrancis285]

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[@asadrking]

You are so helpful!

[@mygoal3441]

The Organic Chemistry Tutor you are too much

[@numairsquestformedicalfutu1017]

8:16 (Wait for bn diverges, may I ask how does that make a sub n diverge? I know we have a finite number in the end). But isn't it a rule that if bn converge then a sub n converge. and if a sub n diverge, then b sub n also diverge? Doesn't it not work the other way around for both conditions. So how is it that b sub n diverge = a sub n diverge? Also thank you for your videos, they really help get things into perspective for calculus! :D

[@dantheman4861]

If Bn diverges and if u take the lim and get 1 which is a finite number then why does An diverge? Ref. 8:10

[@explore5394]

Same doubt

[@alithafer6709]

Because (an) is a power series, its power is the root( √) which is less than 1, since the rule for power series convergence states that P must be >1,(thomas calculus) book-11th edition on page 792. (an) here is divergent.

[@JenniferRokks]

Wish I could like the video 100000x

[@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.

[@irfanoktenoglu4658]

Its good and all but when we have the comparison test, why do we need this?

[@fizzakhan7232]

This only applies when the comparison test rule is flipped -> comparison test rule: bn converges then an converges and an divergent then bn dgt. It can’t be the other way around therefore you apply limit comparison test

[@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

[@Christian-jm5jv]

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

[@ludovico-291hzu]

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

[@sarahdonnelly5236]

@@ludovico-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.

[@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☺️

[@vedantjhawar7553]

Isn't the limit comparison test flawed for some examples? If we were to have the sum from n=1 to infinity of 1/(n^2-1) and tried to evaluate whether it converges or diverges, the closest thing to compare it with would be the sum from n=1 to infinity of 1/(n^2). Using the limit comparison test, we would see that they also reach some value L, so that would mean that since (1/(n^2)) is convergent, 1/(n^2-1) should also be convergent. However, the first value of the sum in 1/(n^2-1) is 1/0, which should make it impossible for them both to converge. Are there some rules that I have missed?

[@SISKCERTWaJaVlogs]

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

[@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

[@pedrosanz8966]

Why does he teach better than the ones with Phd's?

[@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

[@Cobenski4]

Yes I was thinking about that too, maybe you should specifies in parenthesis for an n =/= to 0

[@maryamanayat3350]

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

[@koenabennedict6189]

Thank you

[@rajendramisir3530]

square root of 1/n square = square root of 1/square root of n square = 1/n. Rewrite 1/n in radical form in order to simplify the radical in the denominator.

[@EternalClamness]

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

[@이의진-z5v]

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?

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ur a legend man!

[@curiousityspark3471]

Classmates : "How do you manage a 4.0 GPA? " Me: 👀👀 Organic tutor

[@mingpach2238]

Thank you 🙏🏻

[@AJ-rm7jp]

love you bro

[@cherishnmukubesa4475]

Lovely, keep it up

[@wizben3135]

Thanks so much for everything

[@damonpalovaara4211]

I know the 5 is insignificant in 3^n / 3^n + 5 but that wouldn't fly with my professor (who is super into doing proofs and having us do proofs). The actual method would be to multiply the top and bottom by 1/3^n to get the form 1/(1+5/3^n) which is provably 1

[@ARTDEVGRU247]

That's dumb.

[@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

[@sleverlight]

Why can't you use the normal comparison test for the first one?

[@shiva2608]

in the 8:15, the p series showed it was divergent but the limit comparison approached to 1 which is convergent but you said it was divergent, which one is correct

[@brittniep9219]

Shiva yeah they both either diverge or converge together or are inconclusive so I’m not sure what he meant there either

[@pedrohernandez2379]

@@brittniep9219 im still lost on that part

[@izzytheman20]

Divergent. He made a mistake

[@laila1901]

By the rules of the Limit Comparison Test, if the limit of an/bn= L(a finite number) then it proves the convergence/divergence that is given by separating it in the beginning. By using the p-series, we were able to determine that bn is divergent. If you do limit comparison and the answer is a finite number, then that shows that an is also divergent. In any other circumstances where you aren't using the limit comparison test, reaching a finite number does show convergence. However, these are the rules only for limit comparison test, he didn't make a mistake. I hope this makes sense.