@@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
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.
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 :)
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
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).
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 RUclips TV with the Organic Chemistry Tutor.
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 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!
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! ✍🏻❤️
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
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.
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! 🤲🤲
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
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.
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.
@@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.
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☺️
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.
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.
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?
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
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
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?
@@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
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?
i don't understand why its possible to just take away a constant. When I do that it's wrong, and then when I find a problem that doesn't seem to work with doing that I don't do it and it's wrong and turns out I have to. I just don't understand when to do so and when not to do so.
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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.
They were talking about sum of 1/3/^n@@onwabadosini2962
@@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
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.
BROOO facts, I’m a mechanical engineer and I can say personally you’re helping the world genuinely🙏🏻🙏🏻
Fact man, I study petroleum engineering, this guy helps me a lot since freshman❤️
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I recommend watching the direct test first and then the limit one because it’s easier to understand
100% true
u are 100% correct
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
Whenever I have confusion, I search your video and understand what going on. Thanks bro!
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 :)
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
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!!
fail
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
Organic chemistry is a life saver
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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).
Thank you!!
thanks! couldn't have said it better
You mean the one before last?
I get so happy every time a see you made a video on a subject I need to study 🙏
I love you, thanks for the videos. I wouldn't be passing calc 2 otherwise- your videos are well explained and concise!
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 RUclips TV with the Organic Chemistry Tutor.
You're the OG homie. Thank you once AGAIN for enlightening us peasants about another math concept. Keep rocking man!
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.
Did you pass the semester
@@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.
@@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 😭🙏
@@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!
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.
I'm curious too...can't just leave us hanging dude
I guess you didn't learn the limit comparison test as well as you had hoped.
How did you do?!?
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 😂
@@kelvincheng999 you give me hope, I have a calc 2 midterm tomorrow and hopefully will pass.
The way you teach is INSANE ! 😍
Amazing video, literally running through my math problems because of your extraordinary explanations! Thank you!
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! ✍🏻❤️
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
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.
Thanks my guy, I usually watch khan, but this filled a lot of gaps in my understanding that i couldn't get with khan.
I love you, never gonna stop loving you, youre getting me through calculus and into an engineering degree.
last problem can be solved using direct comparison test
really appreciate your effort man, thanks.
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
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! 🤲🤲
Thanks! I was looking for how to solve one of these problems algebraically and what you did made perfect sense.
You’re AMAZING you make everything so much easier i loved it! Thank you so much
your voice is so soothing .i'm so happy i found your channel
Man has been saving me the past 7 years🙏😭
You are saving my university grades for Calc II. I love you!
Got my final in 6 minutes and ofc this guy saves the day again haha
Thanks again OCT. I can now sleep soundly in my bed knowing how to execute the LCT. You are the best.
Dude thanks again. I was struggling with this, but thanks to you I’m back on track. 🐐
You are the best professor I have ever seen .
❣
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
thank you!
how do we know if we should use the limit comparison test or the direct comparison test?
If one doesn’t work, then use the other
@@Cobenski4 ty
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!
What did you make in orgo? i take it next semester
i just became your fan ....after watching "comparison tests videos".....what an explanation👌👌....love you Sir 🙏
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Watching you from Brazil, you're the best
Thanks you so much for making these videos! They really help!
Youre the reason I'm passing with A's on exams in Calc 2
imagine getting A's in calc 2..i wish.
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@@adansilva6851 good luck :, )
Aww! I literally just had my test 3 hours ago! It’s okay tho, I still love you ♥️
Hope you scored high!
excelente video, muy practico para el aprendimiento rapido.
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)
if i can get through my physics program, i will be proud to say that youre basically my instructor 😊
sa makakita ani nga cmate, hiiii
Thanks for the video! You are an awesome teacher!
You are my math god
I’ve been watching this dude for years now 💀
Literally carrying me 😂
WHAT KIND OF LEGEND ARE YOU
Thank u sooo much sir for ur kindness and for helping us
wouldn't the example at 8:17 be solvable through the direct comparison test?
So would the first example.
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.
Best teacher everrrrr
I feel like I know this dude from around the way or something. Appreciate you bro!
Came for the profile picture, stayed for your playlists
@@bugfact9279 Lol appreciate that, just tryna be great
just a heads up, you have the harmonic series at 5:49 going from 0 to inf.. but its undefined at zero
Thank you sooooo much
just think math easy after you men ....too much respect for your work lol
You are a life saver, Thank you !
يسطا لو فهمتها ياريت تشرحهالي عليا اختبار بعد بكرا ده الانستا بتاعي . (_5stc) ولو ملقتهوش خد ده endl9
@@moazosama معلش والله مخدتش بالي من الريبلاي إلا دلوقتي سوري😂. أتمنى تكون أديت كويس.
I'm just wondering, but isn't the last problem technically a Direct Comparison Test?
@@mundheral-ahmadi8939 I was thinking the same thing. I think he's just taking it one step further.
you sir have blessed me
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.
Thank you so much for this
carrying my degree rn
Thank you, but I think the summation in the series b_n should starts from 1 not from zero.
Bravo, maestro
How can you teach soooo efficiently
you are a life saver
💌
Thank you
You are awesome, sir. Keep it up!
Excelent explanation sir
The Organic Chemistry Tutor you are too much
Can anyone please explain the step at 6:55? When he multiplied the top and bottom by 1/n. Thanks!
if you understand that, can you please explain it to me?
@@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.
You are so helpful!
U help me a lot thanks for that
Thank you, sir.
FAIRA Fa Hey, @8:53, do you know how 1/3^n became (1/3)^n? Thanks
@@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.
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☺️
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
Same doubt
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.
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.
Classmates : "How do you manage a 4.0 GPA? "
Me: 👀👀 Organic tutor
Wish I could like the video 100000x
ur a legend man!
love you bro
4:47 not to mention 1/n^3 is bigger than a of n so DCT would work too
Thank you 🙏🏻
man thankyou!!
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?
On example 2 I’m confused how you chose to divide by 1/n and sqrt of 1/n^2
Why can't you use the normal comparison test for the first one?
What is the some real-life application of comparison test?with examples.
awesome may good give you what you want
Its good and all but when we have the comparison test, why do we need this?
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
You are amazing!!!
Lovely, keep it up
8:08 the harmonic series diverges and the original series has a finite limit which is 1 and thus converges. Clear up the misconception
thanks man a lot
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
That's dumb.
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?
Ryan if you know Bn diverges and you do the test and get a finite number then An also diverges.
6 months later I still wonder
Parker Mell and if you dont get a finite number?
@@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
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?
bingo
Thanks so much for everything
i don't understand why its possible to just take away a constant. When I do that it's wrong, and then when I find a problem that doesn't seem to work with doing that I don't do it and it's wrong and turns out I have to. I just don't understand when to do so and when not to do so.
love u man