Limit Comparison Test
Рет қаралды 735,291
Күн бұрынThis 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:
• 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...
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Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections
@TheOrganicChemistryTutor Жыл бұрын
Next Video: kzfaq.info/get/bejne/erh_ZM6BuZrNg2w.html Final Exams and Video Playlists: www.video-tutor.net/
@onwabadosini2962 Жыл бұрын
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 9 ай бұрын
They were talking about sum of 1/3/^n@@onwabadosini2962
@user-qv1li5qn5u 3 ай бұрын
@@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 4 жыл бұрын
Bro you are really making the difference in this world. Thank you for helping us.. Tomorrow's Engineers and other professionals would always keep you in ours minds, because you just made it easy for us to closed the open gaps in the concept.
@InevitableBingo 2 жыл бұрын
BROOO facts, I’m a mechanical engineer and I can say personally you’re helping the world genuinely🙏🏻🙏🏻
@mouhamethba9305 2 жыл бұрын
Fact man, I study petroleum engineering, this guy helps me a lot since freshman❤️
@JesusMartinez-zu3xl 2 жыл бұрын
@@mouhamethba9305 petroleum and chemical engineers are built different.
@InevitableBingo 2 жыл бұрын
@@JesusMartinez-zu3xl Whatchu know about the P.E. Engine License with M.B.A program for Facilities Engineering😳😂 Edit: nothin
@InevitableBingo 2 жыл бұрын
@@JesusMartinez-zu3xl Mechanical Engineering 💪 , Bio-Med 😵💫🤓, Electrical 🥸, Civil 🤡🤡🤡
@reganmian 11 ай бұрын
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 4 жыл бұрын
I recommend watching the direct test first and then the limit one because it’s easier to understand
@davidthomas5077 3 жыл бұрын
100% true
@avthecool129 5 ай бұрын
u are 100% correct
@yesufhassen7422 5 жыл бұрын
Whenever I have confusion, I search your video and understand what going on. Thanks bro!
@laila1901 4 жыл бұрын
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 3 жыл бұрын
Thank you!!
@justins7796 2 жыл бұрын
thanks! couldn't have said it better
@jaimeirigoyenlopez5884 2 жыл бұрын
You mean the one before last?
@zxynb Жыл бұрын
how do we know if we should use the limit comparison test or the direct comparison test?
@kelvinmasasire6737 Жыл бұрын
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. 3 жыл бұрын
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 :)
@coloredpandas1993 6 жыл бұрын
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 5 жыл бұрын
fail
@sleverlight 5 жыл бұрын
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
@hamzarajab6281 4 жыл бұрын
Organic chemistry is a life saver
@Jackielikagovernor 3 жыл бұрын
@Tshilady Tshilady you really took all the time in the world to respond to some fucker from 2 years ago and said something mean???
@rockmatt9406 3 жыл бұрын
@@Jackielikagovernor ur the mean dude here lmao
@bunny-bunny-bunny 5 жыл бұрын
I love you, thanks for the videos. I wouldn't be passing calc 2 otherwise- your videos are well explained and concise!
@JManTheOddball132 4 жыл бұрын
You're the OG homie. Thank you once AGAIN for enlightening us peasants about another math concept. Keep rocking man!
@georgesadler7830 2 жыл бұрын
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 KZfaq TV with the Organic Chemistry Tutor.
@ghadah3916 5 жыл бұрын
You’re AMAZING you make everything so much easier i loved it! Thank you so much
@FlamingFlareon 4 жыл бұрын
Thanks! I was looking for how to solve one of these problems algebraically and what you did made perfect sense.
@herishbadal3719 6 жыл бұрын
The way you teach is INSANE ! 😍
@pfeliciano4062 4 жыл бұрын
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! ✍🏻❤️
@shaunt1309 5 жыл бұрын
Thanks you so much for making these videos! They really help!
@sahilkatta8490 3 жыл бұрын
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
@tomveer9885 2 жыл бұрын
wouldn't the example at 8:17 be solvable through the direct comparison test?
@ephemeronchimera 10 ай бұрын
So would the first example.
@arianeparadis6439 3 жыл бұрын
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 2 жыл бұрын
Did you pass the semester
@arianeparadis6439 2 жыл бұрын
@@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 2 жыл бұрын
@@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 2 жыл бұрын
@@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!
@kelvincheng999 6 жыл бұрын
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 5 жыл бұрын
I'm curious too...can't just leave us hanging dude
@asadrking 4 жыл бұрын
I guess you didn't learn the limit comparison test as well as you had hoped.
@rahula985 2 жыл бұрын
How did you do?!?
@kelvincheng999 2 жыл бұрын
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 😂
@eliseopachucalazo3167 Жыл бұрын
@@kelvincheng999 you give me hope, I have a calc 2 midterm tomorrow and hopefully will pass.
@collinpowell5412 7 ай бұрын
Man has been saving me the past 7 years🙏😭
@6stringski373 3 жыл бұрын
Dude thanks again. I was struggling with this, but thanks to you I’m back on track. 🐐
@kirbymia6209 5 жыл бұрын
Thanks for the video! You are an awesome teacher!
@michaelbanks1000 3 жыл бұрын
I love you, never gonna stop loving you, youre getting me through calculus and into an engineering degree.
@AngelSoft-ex4wd 4 ай бұрын
Amazing video, literally running through my math problems because of your extraordinary explanations! Thank you!
@Christian-jm5jv 2 жыл бұрын
Can anyone please explain the step at 6:55? When he multiplied the top and bottom by 1/n. Thanks!
@bilinmezevren-291hzu Жыл бұрын
if you understand that, can you please explain it to me?
@sarahdonnelly5236 Жыл бұрын
@@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.
@PK-wr6kz 3 жыл бұрын
Can anybody suggest where I can see more such examples as shown in this video using this specific technique ?
@Vincent-KN Жыл бұрын
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.
@priyankabm7458 2 жыл бұрын
your voice is so soothing .i'm so happy i found your channel
@mayrahernandez9911 5 жыл бұрын
Thank you so much for this
@leahbronstein9205 5 жыл бұрын
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?
@Ali_Pxll Жыл бұрын
last problem can be solved using direct comparison test really appreciate your effort man, thanks.
@cloudyo_o2792 2 жыл бұрын
carrying my degree rn
@christinatimalsina5584 9 ай бұрын
You are the best professor I have ever seen . ❣
@_kevin_wong_ 2 жыл бұрын
Got my final in 6 minutes and ofc this guy saves the day again haha
@carolynncalin1199 Жыл бұрын
You are saving my university grades for Calc II. I love you!
@fatmacdacat 3 жыл бұрын
Thanks again OCT. I can now sleep soundly in my bed knowing how to execute the LCT. You are the best.
@marcosjohnsonnoya417 3 жыл бұрын
Thanks my guy, I usually watch khan, but this filled a lot of gaps in my understanding that i couldn't get with khan.
@sawairajamil1617 3 жыл бұрын
Thank u sooo much sir for ur kindness and for helping us
@wisemantottee362 5 жыл бұрын
You are awesome, sir. Keep it up!
@Lauren-cv6ky 4 жыл бұрын
you sir have blessed me
@hannanbaig7888 5 жыл бұрын
Why do you multiply the numerator and denominator with 1/n at 6:55?
@asadrking 4 жыл бұрын
You are so helpful!
@luissanoja6096 3 ай бұрын
excelente video, muy practico para el aprendimiento rapido.
@beachwave5705 2 жыл бұрын
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
@samueldarenskiy6893 7 ай бұрын
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?
@zainabinam2636 4 жыл бұрын
Thank you sooooo much
@ruymorais3409 Жыл бұрын
Watching you from Brazil, you're the best
@juancarrillo6993 5 жыл бұрын
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)
@MyDavidrock 3 жыл бұрын
just a heads up, you have the harmonic series at 5:49 going from 0 to inf.. but its undefined at zero
@lordfarquaadreal9156 2 жыл бұрын
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! 🤲🤲
@MariaCaro95 6 жыл бұрын
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!
@fatcammal 6 жыл бұрын
What did you make in orgo? i take it next semester
@Alex-kd4vo Жыл бұрын
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.
@davidfrancis285 4 жыл бұрын
U help me a lot thanks for that
@EternalClamness Жыл бұрын
On example 2 I’m confused how you chose to divide by 1/n and sqrt of 1/n^2
@aleemprince3771 5 жыл бұрын
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"?
@inuyasha11p 6 жыл бұрын
@The Organic Chemistry Tutor how would u remove significance if the numerator has a trig such as sin(n)
@inuyasha11p 6 жыл бұрын
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.
@kevint681 5 жыл бұрын
Youre the reason I'm passing with A's on exams in Calc 2
@megsperry2925 3 жыл бұрын
imagine getting A's in calc 2..i wish.
@adansilva6851 3 жыл бұрын
@@megsperry2925 fr lmaoooo, only in my dreams
@megsperry2925 3 жыл бұрын
@@adansilva6851 I'm only just trying to pass..with a nice 'ol C
@adansilva6851 3 жыл бұрын
@@megsperry2925 im aiming for a high grade but as long as I pass, i'll take it
@megsperry2925 3 жыл бұрын
@@adansilva6851 good luck :, )
@namehere630 3 жыл бұрын
thank you so much!
@intkayne736 3 жыл бұрын
Thank you
@mingpach2238 4 жыл бұрын
Thank you 🙏🏻
@alicesze1360 3 жыл бұрын
Best teacher everrrrr
@samanthac2216 5 жыл бұрын
You are my math god
@janem8664 5 жыл бұрын
I'm just wondering, but isn't the last problem technically a Direct Comparison Test?
@Zyngawf9 4 жыл бұрын
@@mundheral-ahmadi8939 I was thinking the same thing. I think he's just taking it one step further.
@MMIST7 5 жыл бұрын
7:35 im so losttt where did 1/n and radical1/n^2 come from????'
@themansans1929 5 жыл бұрын
multiply by a fancy 1, the SQRROOT of 1/n^2 is equal to 1/n, this gets the n in the denominator so when we take the limit, it can go to zero
@darcash1738 Жыл бұрын
Bravo, maestro
@cenkocenk Жыл бұрын
thank you
@syedalauddinbukhari9801 2 жыл бұрын
can anyone explain 4:39 STEP where we have limit as 1?
@Alifaga 2 жыл бұрын
WHAT KIND OF LEGEND ARE YOU
@beetogarcia9983 4 ай бұрын
I’ve been watching this dude for years now 💀 Literally carrying me 😂
@AlbertoRivas13 4 жыл бұрын
Excelent explanation sir
@hermannebbinghaus3040 6 жыл бұрын
Aww! I literally just had my test 3 hours ago! It’s okay tho, I still love you ♥️
@tokamak4219 6 жыл бұрын
Hope you scored high!
@kxvix8774 2 жыл бұрын
you are a life saver 💌
@iigreenstarii 3 жыл бұрын
You are a life saver, Thank you !
@moazosama 3 жыл бұрын
يسطا لو فهمتها ياريت تشرحهالي عليا اختبار بعد بكرا ده الانستا بتاعي . (_5stc) ولو ملقتهوش خد ده endl9
@iigreenstarii 3 жыл бұрын
@@moazosama معلش والله مخدتش بالي من الريبلاي إلا دلوقتي سوري😂. أتمنى تكون أديت كويس.
@blissnotes3477 2 жыл бұрын
if i can get through my physics program, i will be proud to say that youre basically my instructor 😊
@blissnotes3477 2 жыл бұрын
sa makakita ani nga cmate, hiiii
@mr.prince8701 6 жыл бұрын
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 6 жыл бұрын
Ryan if you know Bn diverges and you do the test and get a finite number then An also diverges.
@kylesteele5848 5 жыл бұрын
6 months later I still wonder
@saif0316 5 жыл бұрын
Parker Mell and if you dont get a finite number?
@Bamberosjose 5 жыл бұрын
@@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
@maryamanayat3350 4 жыл бұрын
What is the some real-life application of comparison test?with examples.
@vedantjhawar7553 3 жыл бұрын
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?
@lavina3535 4 жыл бұрын
does an have to be smaller than bn?
@amirwagih4797 3 жыл бұрын
ur a legend man!
@kellyh6359 Жыл бұрын
For the first example, since is bn is a bigger series and converges couldn't you say the an series converges by regular comparison test?
@aboutdogzoffcial 10 ай бұрын
man thankyou!!
@numairsquestformedicalfutu1017 9 ай бұрын
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
@BhajanandArti 5 жыл бұрын
i just became your fan ....after watching "comparison tests videos".....what an explanation👌👌....love you Sir 🙏 👉love from India ✌️👌
@wizben3135 Жыл бұрын
Thanks so much for everything
@MatthewAyoob 4 жыл бұрын
You are amazing!!!
@warwick802 Жыл бұрын
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 Жыл бұрын
thank you!
@santoshupretimadara 5 жыл бұрын
thanks man a lot
@user-sf8wg4qf4t 3 жыл бұрын
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?
@misssaleem5139 2 жыл бұрын
Sir how to take bn in limit comparison test
@breannag3055 5 жыл бұрын
how do u know whether to use direct comparison or limit comparison? is it just what you see first or preference or something
@PuertoRicanCoquiLHCD 5 жыл бұрын
It’s more of a preference, you can use whatever test you find easier
@matthewgrove2770 3 жыл бұрын
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 Жыл бұрын
bingo
@nicholasmaloof8378 4 жыл бұрын
10:37 is there anything proving we can disregard that 5 in the denominator? I believe your logic, but just want something more formal if I'm justifying this on the test
@Lauren-cv6ky 4 жыл бұрын
When taking the limit as n approaches infinity the 5 in the denominator is insignificant because a number raised to an infinite power is extremely massive and the 5 doesn't affect the term that has the n.
@AJ-rm7jp Жыл бұрын
love you bro
@ethanvirtudazo1657 2 жыл бұрын
10:30 Why can we just dismiss the 5 here in the denominator (3^n + 5) but not the 2 in the (n^2 + 2) in the previous problem? Would appreciate any help:)
@AshrZ 2 жыл бұрын
Actually, you *can* dismiss the 2 in the n^2+2 from the previous problem - it makes no impact on the limit as it approaches infinity.
@faichalayeva3677 5 жыл бұрын
Thank you, sir.
@uzumakikuroko9000 5 жыл бұрын
FAIRA Fa Hey, @8:53, do you know how 1/3^n became (1/3)^n? Thanks
@faichalayeva3677 5 жыл бұрын
@@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 5 жыл бұрын
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☺️
@DarkSpydaIV 4 жыл бұрын
How do we know which one is supposed to be a sub n and which one should be b sub n?
@dantheman4861 4 жыл бұрын
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 2 жыл бұрын
Same doubt
@alithafer6709 Жыл бұрын
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.
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