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 🙏🙏
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
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!
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 TH-cam TV with the Organic Chemistry Tutor.
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
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?
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".
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?
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.
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.
I have a question: is it true that whenever we want to determine the monotonicity of a sequence {a_n} we could always use the Calculus method of taking derivative of continuous function f(x) with f(n) = a_n? And if f(x) is increasing on an interval then {a_n} is increasing on that interval and vice versa if f(x) is decreasing on an interval then {a_n} is decreasing on that interval? Is this obvious or is there some theorem/corollary stating this?
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😊😊7😊+
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....
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
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
That one guy who covers 3 chapters in one hour🔥🔥🔥🔥🙏🙏👌🌹✨
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 :)
/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 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!?!?
your accent is so wholesome, i love it
The way you teach restores my love for Math😳
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
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!
You keep my knowledge increasin'
Today is year 2023 and this video is timeless. Very helpful, thank you for this.
Explained better than my book did. Good job!
Words are not enough to express my gratitudes to you! Much thanks from South Sudan
THANK YOU SO MUCH BUDDY
Thanks in a million. Where have you been all these years!
Sir your lecture is so evident that, after listening it I haven't found any doubt.
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 TH-cam TV with the Organic Chemistry Tutor.
king of helping me learn calc during quarantine
I'm from Kenya and I like watching your videos. Good job
EVERYONE PRAISE THE ORGANIC CHEMISTRY TUTOR
Thanks for explaining so clearly. My professor throws a bunch of complicated logic and formulas only to explain this simple topic.
hi (sorry for bad math)
hi, sorry at least u have nice body (i saw ur tiktok of u no shirt on hehe :3)
A brilliant video with very clear explanations. Thank you.
The guy who teached me the most of my high school chemistry and maths...
This just saved my day
you saved my life thaaks I'm from ethiopia
You're the best of all time, much respect boss, from physics, maths and chemistry oh so amazing....
You’re one of my greatest inspirations ❤️♾
you helped me to get my degree, bro!
calculus 2 ota yi tu manga 😭😭 out here thinking i dont know what monotonics ate but thanks to him i got
Thank you this was very helpful! at the right pace and the problems you chose were great!
Your the best tutor 😭
*smacks the table* THANK YOU! Thank you very much... Finaly!
when I open any math on youtube then I realise its not your voice I just cancel. THATS WHY I HAD TO SUBSCRIBE
You are a legend. Thank you very much
You clearly explained everything, thank you so much bro.
exams tomorrow! helped me quite a bit :D
Thanks... I learnt many things about this lecture now
my appreciation for you do be increasin'
These videos are the best
you are the best mr
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
Thank you very much for this .love from india
muhammad was NOT the last prophet, you are.🙏🙏🙏
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
Thanks so much, it is very helpful
28:00 I see what u did with that factorial. SMART!
Can you do a video about lower, upper, LUB and GL bounds
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
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
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?
Very helpful 👍🏻
Thank you ❤
always a helping tutor than you
This guy explains a thousand tumes better than my prof bruh
Albert Einstein
How to do math??
Step 1= write the question.
Step 2= cry....
Quality content 😍
sir i have no Idea with video really befire this video thus consept was very bad but now it is very good👍
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".
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
If a sequence is bounded but not monotonic, it might converge or it might diverge
Sir very well done.. Great explanation
I love you so much for making this video
Why don't you make a separate video on complete bolzano-weierstrass theorem
thank you i enjoyed this!
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
Very clear
Your a legend
1:10 doesn't that make a horizontal line both increasing and decreasing?
Thankyou for the video
What about 1/x where the sequence is bounded and is always decreasing monotonic but is divergent? Doesn’t that break the rule?
Can you just take the derivative to show that’s either increasing or decreasing. If positive increasing… if negative dec
Very good
God bless you
This was very good
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 again ❤️❤️
Thanks!
Nice explation keep it up
n-> infinite, Lim An = 0, which doesn't guarantee it converges.
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.
if d(an)/dn is positive can we confirm that a function is monotically increasing?
so monotonic functions can have constant sections?
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.
I have a question: is it true that whenever we want to determine the monotonicity of a sequence {a_n} we could always use the Calculus method of taking derivative of continuous function f(x) with f(n) = a_n? And if f(x) is increasing on an interval then {a_n} is increasing on that interval and vice versa if f(x) is decreasing on an interval then {a_n} is decreasing on that interval?
Is this obvious or is there some theorem/corollary stating this?
If f(x) is differentiable, then this certainly holds
Why should the monotonic sequence at 11:45 be greater than or equal to, shouldn't it just be greater than?
18:00 a mistake. It should be n >= -1/2
Very nice thanks 👌
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
Very helpfull 💕💕
Thanks in a million!
Why did you add instead of distribute the "2" in the denominator at 5:52
thank u very much
Bruh. In the end he’s like *mic drop*🎤