I just want ot say, of all the people out there this guy will one day be able to claime that he is responsable for a whole generation of college students becoming engineers and passing. Thanks man your a God send
Am Chris, studying Data Sciences in Germany. I must say a very big thank you for simplifying complex mathematical problems. You're a legend. I appreciate you
Whenever I see something difficult mathematical problems I know this guy has an ultimate solution to make it easier and simple... this guy have millions trillions of students who are praying for you every second of a day..may God bless you every second of your life Aameen
/after watching your videos, finally my mindset about calculus was hard had changed. the way you teach is more specific than my lecturer did and i understand this a lot. Thank you so much!!!!!! (sorry for my bad english)
I'm literally from Finland and your videos have been the most helpful in my studies which are all in Finnish. The terms are pretty close anyways, but there isn't a better tutor in Finland either so I'm thankful that I can understand English 🙏🙏
YOU ARE JUST TEACHING ME WHAT I WANT!! OMG THANK YOU! you saved my first of career lol, my calculus teacher just give us a ton of pdfs with lots of letters... But you made me understand everything with graphs and so! Ty again!
Another topic you put to shame my calc 2 teacher at. He puts no effort in teaching and notes are rushed written for someone who is already a master at the topic. Thank you so much
Professor Organic Chemistry Tutor, thank you for explaining Monotonic Sequences and Bounded Sequences in Calculus Two. I also encountered Monotonic and Bounded Sequences in Advanced Calculus; however, I did not understand Monotonic/Bounded Sequences until I watched and analyzed this great video from start to finish. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Just a clarification, at 30:51, you said it is convergent when n starts at 2. But regardless the value of n (whether it is positive or negative), it is no longer convergent, right?
On my calculus textbook by James Stewart, it says that a sub n is less than a sub n+1. But you said a sub n is less than or equal to a sub n+1. Your definition contradicts the textbook. But great video overall
I thought, because of the growth rate theorem, n! infinity 3^n/n! would be an infinite series. Thus would make it a monotonic, lower bounded, divergent series
18:16 why do we have n>=1? Like, if we solve the inequality, the value that comes is -1/2, but if we consider only whole numbers, why didn't we put n>=0? @TheOrganicChemistryTutor
I know this is a month old but I believe it is due to the fact that Calc 2 will not include negative values for a nth term. So the original problem is a fraction with n as the denominator and therefore we cannot start n from 0 or else it is undefined. So instead we start it from the 1st term n=1 and go up from there.
Is there a tip/trick for me to keep up with the math needed to understand this better? I find myself understanding things when he specifically explains them (in detail) but If I was supposed to intuitively get it right I just wouldn't have it on my mind. Thanks!
If you're talking about the algebraic tricks he used, such as manipulating inequalities, I couldn't hope to explain it better than @TheOrganicChemistryTutor. However, my main takeaway from the entire video is that a sequence converges when it is bounded and monotonic. A bounded sequence is a sequence that has a floor and ceiling (lower and upper bounds) as n goes to infinity. A monotonic sequence is a sequence that only increases or only decreases in the long run. Note how in the last example, the sequence wasn't monotonic on n >= 1, but it was monotonic on n >= 2.
I find the concepts of sequences bounded above and/or bounded below kind of hard to understand because the semantic is kind of counter-intuitive for instance bounded below means that the sequence has a lower bound, but from face value it sounds like the sequence would be below a limit by the words "bounded below".
I have a question What if the sequence is bounded above but it is decreasing function Still it is monotonic and also bounded but will it be convergent?
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I just want ot say, of all the people out there this guy will one day be able to claime that he is responsable for a whole generation of college students becoming engineers and passing. Thanks man your a God send
Truly we are all of us blessed this day.
You really boosted my knowledge 😊
huh?! since when@@oytanali1803
and biologists
Cringe
I think this guy is one of the best tutors in the world. I appreciate your works a lot. Kudos, you doing a great work....
Am Chris, studying Data Sciences in Germany. I must say a very big thank you for simplifying complex mathematical problems. You're a legend. I appreciate you
Whenever I see something difficult mathematical problems I know this guy has an ultimate solution to make it easier and simple... this guy have millions trillions of students who are praying for you every second of a day..may God bless you every second of your life Aameen
Im getting so close. Im going to finish every last one of the 226 videos in your calculus playlist.
@Alex Lerch oh yeah. i finished all of them + the middle/highschool mathematics all together in like 9 months or something.
@@kameronbriggs235 ححذججطططط
Gg bro
Great
Goddamn, let’s go
That one guy who covers 3 chapters in one hour🔥🔥🔥🔥🙏🙏👌🌹✨
/after watching your videos, finally my mindset about calculus was hard had changed. the way you teach is more specific than my lecturer did and i understand this a lot. Thank you so much!!!!!! (sorry for my bad english)
I had an emergency surgery (appendectomy) mid-semester and missed about a week of classes, and these videos are helping me get caught up! Thanks!
I hope you feel better :)
I just wanted to let you know, you saved my life! You're amazing!
I'm literally from Finland and your videos have been the most helpful in my studies which are all in Finnish. The terms are pretty close anyways, but there isn't a better tutor in Finland either so I'm thankful that I can understand English 🙏🙏
ya thats cool and all, but... can you understad finnish??
What? You are stealing!?!?
YOU ARE JUST TEACHING ME WHAT I WANT!! OMG THANK YOU! you saved my first of career lol, my calculus teacher just give us a ton of pdfs with lots of letters... But you made me understand everything with graphs and so! Ty again!
The way you teach restores my love for Math😳
your accent is so wholesome, i love it
Words are not enough to express my gratitudes to you! Much thanks from South Sudan
You keep my knowledge increasin'
Thanks in a million. Where have you been all these years!
Explained better than my book did. Good job!
Another topic you put to shame my calc 2 teacher at. He puts no effort in teaching and notes are rushed written for someone who is already a master at the topic. Thank you so much
Today is year 2023 and this video is timeless. Very helpful, thank you for this.
THANK YOU SO MUCH BUDDY
king of helping me learn calc during quarantine
Thanks!
Thanks for explaining so clearly. My professor throws a bunch of complicated logic and formulas only to explain this simple topic.
A brilliant video with very clear explanations. Thank you.
I'm from Kenya and I like watching your videos. Good job
Sir your lecture is so evident that, after listening it I haven't found any doubt.
The guy who teached me the most of my high school chemistry and maths...
You’re one of my greatest inspirations ❤️♾
Thank you this was very helpful! at the right pace and the problems you chose were great!
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First time understanding this, uh are an outstanding guy thanks
EVERYONE PRAISE THE ORGANIC CHEMISTRY TUTOR
you helped me to get my degree, bro!
this is really helpful , thank you so much
You clearly explained everything, thank you so much bro.
Your the best tutor 😭
You are a legend. Thank you very much
Professor Organic Chemistry Tutor, thank you for explaining Monotonic Sequences and Bounded Sequences in Calculus Two. I also encountered Monotonic and Bounded Sequences in Advanced Calculus; however, I did not understand Monotonic/Bounded Sequences until I watched and analyzed this great video from start to finish. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
*smacks the table* THANK YOU! Thank you very much... Finaly!
Thanks... I learnt many things about this lecture now
Thanks so much, it is very helpful
calculus 2 ota yi tu manga 😭😭 out here thinking i dont know what monotonics ate but thanks to him i got
These videos are the best
hi (sorry for bad math)
hi, sorry at least u have nice body (i saw ur tiktok of u no shirt on hehe :3)
exams tomorrow! helped me quite a bit :D
you saved my life thaaks I'm from ethiopia
28:00 I see what u did with that factorial. SMART!
Sir very well done.. Great explanation
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Thank you ❤
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my appreciation for you do be increasin'
I love you so much for making this video
26:47 isn't this incorrect. by the definition of a monotonic series a_n >= a_n+1 or a_n
I’m also quite confused by this, since I’ve only ever seen that as the definition, when it clearly does not work here
It strictly decreases after the value n = 2.
thank you i enjoyed this!
Just a clarification,
at 30:51, you said it is convergent when n starts at 2.
But regardless the value of n (whether it is positive or negative), it is no longer convergent, right?
Yes
Thank you again ❤️❤️
Can you do a video about lower, upper, LUB and GL bounds
1:10 doesn't that make a horizontal line both increasing and decreasing?
Thankyou for the video
Very good
On my calculus textbook by James Stewart, it says that a sub n is less than a sub n+1. But you said a sub n is less than or equal to a sub n+1. Your definition contradicts the textbook. But great video overall
20:45 that doesn't mean that the sequence converges if the limit found is 0. It's when the function an converges that its limit is 0
sir i have no Idea with video really befire this video thus consept was very bad but now it is very good👍
I thought, because of the growth rate theorem, n! infinity 3^n/n! would be an infinite series. Thus would make it a monotonic, lower bounded, divergent series
Nice explation keep it up
always a helping tutor than you
Very helpfull 💕💕
This was very good
Very nice thanks 👌
Why did you add instead of distribute the "2" in the denominator at 5:52
This guy explains a thousand tumes better than my prof bruh
Thanks
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18:16 why do we have n>=1? Like, if we solve the inequality, the value that comes is -1/2, but if we consider only whole numbers, why didn't we put n>=0? @TheOrganicChemistryTutor
I know this is a month old but I believe it is due to the fact that Calc 2 will not include negative values for a nth term. So the original problem is a fraction with n as the denominator and therefore we cannot start n from 0 or else it is undefined. So instead we start it from the 1st term n=1 and go up from there.
when I open any math on youtube then I realise its not your voice I just cancel. THATS WHY I HAD TO SUBSCRIBE
Very clear
Why should the monotonic sequence at 11:45 be greater than or equal to, shouldn't it just be greater than?
Your a legend
Is there a tip/trick for me to keep up with the math needed to understand this better? I find myself understanding things when he specifically explains them (in detail) but If I was supposed to intuitively get it right I just wouldn't have it on my mind. Thanks!
If you're talking about the algebraic tricks he used, such as manipulating inequalities, I couldn't hope to explain it better than @TheOrganicChemistryTutor. However, my main takeaway from the entire video is that a sequence converges when it is bounded and monotonic. A bounded sequence is a sequence that has a floor and ceiling (lower and upper bounds) as n goes to infinity. A monotonic sequence is a sequence that only increases or only decreases in the long run. Note how in the last example, the sequence wasn't monotonic on n >= 1, but it was monotonic on n >= 2.
Bruh. In the end he’s like *mic drop*🎤
15:59 i couldn't understand what he said and I don't know how he did that. can someone help me please?
1/x^2 is the same as x^-2 so derivative of x^-2 is -2x^-3 which is simply -2/x^3
Thanks in a million!
God bless you
Hello,
From my experience it doesn’t appear to be a good strategy to assume that an
You make the assumption based on your observation by plugging in the numbers.
He should have proved it by mathematical induction
Hello Organic Chemistry Tutor! In your last example, you said that the sequence IS monotonic even though it's increasing for n
It has a monotonic tail, and if a sequence is bounded and has a monotonic tail, it is also convergent.
Its wring he did it wrong
so monotonic functions can have constant sections?
15:53 How is this "bounded, this only has a lower bound?
thank u very much
Thank you sir
9:50 why are we dividing an/an+1, because on the first problem we did not have to divide so I am confused on that.
Because the sequence is decreasing.
Why don't you make a separate video on complete bolzano-weierstrass theorem
I find the concepts of sequences bounded above and/or bounded below kind of hard to understand because the semantic is kind of counter-intuitive for instance bounded below means that the sequence has a lower bound, but from face value it sounds like the sequence would be below a limit by the words "bounded below".
I have a question
What if the sequence is bounded above but it is decreasing function
Still it is monotonic and also bounded but will it be convergent?
around 28:30 shouldn't it be n-1?
The graph at minute 14:03 is not monotonic, is it?