I cannot thank you enough! I'm a full time college student living out on his own in an apartment so I work nights from 10PM-6AM five times a week and sometimes miss out on info during lectures. This section has been brutal to me.
Do you realize what a huge help you are to so many people!? You deserve more attention! Thanks for all the videos you make you are my favorite youtube instructor of all time hands down!
An analogy. You are driving home in your car with a friend. The car is low on gas, the low gas light comes on. Your friend lives a few miles before your house, on the way, less distance. If you make it home (converge) of course so did your friend. But if your friend makes it home, that doesn't mean you won't run out of gas on the way to your house (diverge). Same situation here.
Hi! Just wanted to let you know that your channel has been extremely helpful recently!! My calculus teacher passed away in January, and she was one of the best teachers I’ve ever had. I know she would have wanted me to continue working hard in her class, so I’m doing the best I can with your videos and a new teacher. Thanks for all you do!!!
The problem at 11:50ish is true guys because remember we have been given a restriction if n is greater than or equal to 3. So if you were to plug in 3 you can actually see that 1/n is smaller. Also keep in mind that you need to simplify for the second to last problem n/n^2 becomes 1/n
OCT...I hands down, absolutely, without a doubt, attribute every passing grade in my math and science classes to you! Thank you OCT! You down with OCT yeah you know me!
@@rockyk6805 As far as rankings go, it's 7th in the US. Classes are pretty rigorous, but there are a lot of supplemental resources available, and if you do well and get your degree, you can basically count on landing a good job after graduation. Not to mention that it's a leading research university, which opens up a lot of opportunities for undergrad experience. On a more personal level, I do love the school. The people are chill, most of the professors are great (excluding some for the weed-out classes), and it's overall a solid choice.
I have my calculus 2 exam tomorrow and i literally cried because i couldn't understand these.Watching these 9 hours before the exam and man i just wanna say thankyou Allah apki dunya aur akhrat achi karey
I have a question about the graph at 2:20, if the sequence itself is converging but it’s converging to a number above 0 then the series will be divergent , then all the graphs he drew should be divergent?
These vids always help me better understand concepts I don't always understand right away in class. Can you do more examples with trig though? I always feel so confident breezing through the first questions in my textbook but once I get to the problems with lots of trig it's an uphill battle.
hmm.... thanks dude-- i read the book for weeks but they never tell you how the original function 1/2+3^n became 1/3^n and 1/2+3^n | so thanks for using the big function small function analogy.
The section at 11:15 was explained poorly. The point he was trying to make was ln(n) is greater than 1/n once n is > or equal to 3 SINCE ln(n) will THEN be greater than 1/n's numerator, which is simply 1.
At 12:10 why is it allowed to do n >= 3 I thought all Bn terms had to be bigger than An terms. Is it because they are only 2 terms that dont follow that which doesnt affect the whole series because only 2 terms affecting a series of infinite terms is very small relative to it.
The DENOMINATOR is smaller, making the overall fraction bigger. 1/2 is greater than 1/5, even though 5 is greater than 2. When you make each number in its own denominator, it flips the inequality.
Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on the Direct Comparison Test in Calculus Two. This topic in Calculus Two can be problematic, however students must know the different tests and how to apply them in different cases. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
Question: "IN THIS VIDEO," if a sub n is inconclusive, do we leave the answer like that? Do we have to solve further to find if a sub n ("an") is divergent t or convergent?
I don't quite understand how it works in the case of a decreasing series. If bn is larger than an, but both are decreasing then how does bn converging tell us that an also does
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Isn't 1/n convergent
@@Idurangalk 1/n is convergent, but its series is not. Look up p-series to look up more on the topic.
❤
My man is carrying the entirety of the next generation's higher education on his shoulders
fr
The most underrated channel
ikr
@Txawjntse Vang wuzzy
@Txawjntse Vang lol I was not expecting that reply so I actually laughed.
Lmao he has over 2 million subscribers. Most don't take calculus and many avoid it at all costs.
not anymore lmao
I cannot thank you enough! I'm a full time college student living out on his own in an apartment so I work nights from 10PM-6AM five times a week and sometimes miss out on info during lectures. This section has been brutal to me.
aunpaidintern ! Good luck man
How tf did you survive that
All the best bro
wtf when do you sleep
bro best of luck..
Do you realize what a huge help you are to so many people!? You deserve more attention! Thanks for all the videos you make you are my favorite youtube instructor of all time hands down!
An analogy.
You are driving home in your car with a friend. The car is low on gas, the low gas light comes on.
Your friend lives a few miles before your house, on the way, less distance.
If you make it home (converge) of course so did your friend.
But if your friend makes it home, that doesn't mean you won't run out of gas on the way to your house (diverge).
Same situation here.
what a nice way to explain it thanks man
thanks for this, my professor was so confusing when he explained it
Very very nice way to put it 👍
That's deep man😊
10:34
you and patrickjmt are the people i pray to thank you everynight
Honestly though man. The internet is a beautiful thing, i honestly feel bad for people that struggled in math before the internet was a thing.
Sameee ☺️☺️☺️
@@bicboi46 its just something dope doing math
Hi! Just wanted to let you know that your channel has been extremely helpful recently!! My calculus teacher passed away in January, and she was one of the best teachers I’ve ever had. I know she would have wanted me to continue working hard in her class, so I’m doing the best I can with your videos and a new teacher. Thanks for all you do!!!
Hey, good luck and don’t give up! RIP to your awesome calc teacher
The problem at 11:50ish is true guys because remember we have been given a restriction if n is greater than or equal to 3. So if you were to plug in 3 you can actually see that 1/n is smaller.
Also keep in mind that you need to simplify for the second to last problem n/n^2 becomes 1/n
You are just awesome. Consistently through the past year, whenever I've struggled to understand a concept or technique, your videos make it click.
that graph visual really helped me understand things so much clearer! thank you!!!
I can't believe I only now found your videos. They are SO helpful, and make these problems so much easier to understand. Thank you!!!!
I get so sad whenever he says "This is the last example for this video''
you're a life saver, thank you so much 😭❤
I can always count on this channel for the 2am next day exam cram
I don't even have to go to class, I just watch your videos before my quizzes. Good stuff man
Best math channel, been watching a lot of your videos, they are a lot of help. Thank you!
Thank you for doing these!
If you can, please do one on Taylor and Maclaurin series & Power series.
Exam Monday and you’ve helped me ace everything
excellent video. I feel twice as ready for my exam tomorrow.
honestly my best teacher on youtube
OCT...I hands down, absolutely, without a doubt, attribute every passing grade in my math and science classes to you! Thank you OCT! You down with OCT yeah you know me!
8:56 why inconclusive? we didn't check a smaller series but by just a bigger series is divergent we say it's inconclusive?
what else is there to check? You use limit comparison test if you get inconclusive
u r a math god, thank u for humbly serenading us w ur godtier wisdom
@11:44, I don't understand how he arrived at 1/n. Can someone please explain? All in all, it's still a great video :)
because the numerator becomes insignificant compared to the denominatoe?
this man can deadlift an entire graduating class
As an engineering student at Purdue, may you be blessed in all facets of life. We love you.
How is Purdue for engineering?
I was thinking of transferring
@@rockyk6805 As far as rankings go, it's 7th in the US. Classes are pretty rigorous, but there are a lot of supplemental resources available, and if you do well and get your degree, you can basically count on landing a good job after graduation. Not to mention that it's a leading research university, which opens up a lot of opportunities for undergrad experience. On a more personal level, I do love the school. The people are chill, most of the professors are great (excluding some for the weed-out classes), and it's overall a solid choice.
@@hayley863 Hey thanks for the response. I just might see you there if my grades hold up :)
@@hayley863You graduate?
@@vipari I did, but from a different school. I actually ended up transferring to a school in my home state :)
Remember if An=< Bn it will converge unless An goes to negative infinity
I made it to calc 2 and I'm so happy.
I have my calculus 2 exam tomorrow and i literally cried because i couldn't understand these.Watching these 9 hours before the exam and man i just wanna say thankyou Allah apki dunya aur akhrat achi karey
Haha same boat here. Exam is in 21 hours for me
@@Giblet12 *cries in calculus*
Best of luck ✨
@@maktub_txt Thanks my man
I always watch this guys videos before the lectures by my professors... always.
The savior of my calc grade
thanks my teacher you're a good teacheer
Thanks a lot sir 👍. I got cleared the concept of direct comparison test . I wasn't knowing it so clearly .
I love you ❤ you are awesome i had wasted 4hrs trying to understand this you made me understand this in 15 mins.🥺🥺🥺 love you
You saved my life mann great presentation
most loved youtuber fo sho lmao
It really helps , even though I don’t know english
it's another moment of when foreigners say they don't know english but speak way better than the natives.... respect
I LOVE YOU SO MUCH thank you for all the videos!!!
you're so good at teaching
I bet you never thought how important your channel would be
he's gonna save my semester yehe ; -- ;
god bless you man thank you so much from turkey 🇹🇷🇹🇷
LITERALLY SAVING MY LIFE
You are the best, that all what I can say, thank you my legend ❤️
Thanks a lot for saving my calc grades
at 11:53 why didnt you consider ln(n) / n (the bigger series) instead of 1 / n (the smaller series)?
Hannan Baig yeah I was confused, because if you were to plug in any number the bigger one would be 1/n
Oh I figured it’s because we had a restriction of n is greater than or equal to 3
Most concept full channel
I have a question about the graph at 2:20, if the sequence itself is converging but it’s converging to a number above 0 then the series will be divergent , then all the graphs he drew should be divergent?
Thanks is most useful your video than others.
These vids always help me better understand concepts I don't always understand right away in class. Can you do more examples with trig though? I always feel so confident breezing through the first questions in my textbook but once I get to the problems with lots of trig it's an uphill battle.
These videos are so helpful!! Thank you!
What a wonderful lesson. Keep it up.
hmm.... thanks dude-- i read the book for weeks but they never tell you how the original function 1/2+3^n became 1/3^n and 1/2+3^n | so thanks for using the big function small function analogy.
when will he do a face reveal. I've been watching his videos for 2 years and I need to know how he looks like.
tatia a why ?
danny camello I need to put a face to it
He probably looks like an angel
or the face of god
tatia a me too😅😂
The section at 11:15 was explained poorly. The point he was trying to make was ln(n) is greater than 1/n once n is > or equal to 3 SINCE ln(n) will THEN be greater than 1/n's numerator, which is simply 1.
thanks
@@rohhanbhardwaj I’m glad my comment helped someone 😁😁
Amazing explaination
I follow your all the vedios🌝 🥺🥺 again thank you🥺❤😍😘
Thanks a lot. I'm liking the new colors. It looks great
More more more more...🙏 thank you😍🥺😘😘
10:55 why cant we use L'hospital rule when n goes to infinity wouldnt the bid series go to zero ?
Thanks man.You are a life saver
best content ever very usefull thank you for everything
Thank you this was really good and helpful!!!!
I don't know why but 8:35 sounds like the perfect time for some V-sauce music
I would be proud to shake this mans hand
Superbb keep making 👍👍👍👍👍👍👍
Omg thank you very much bro. You helped me
At 12:10 why is it allowed to do n >= 3 I thought all Bn terms had to be bigger than An terms. Is it because they are only 2 terms that dont follow that which doesnt affect the whole series because only 2 terms affecting a series of infinite terms is very small relative to it.
The examples are very simple!!!
Can anybody explain how he got convergence at 5:06? I thought that n
you're probably thinking of the p series test, what he did there was a geometric series
Bro u think of p series
in class i was lost, on hawks i was confused on yt it all makes sense lol thanks
Thank you very much, I hope you keep going up to diff
for 7:59 wouldn't the first one be greater than or equal to the second? Since you're dropping the 4 that one would be smaller no?
The DENOMINATOR is smaller, making the overall fraction bigger. 1/2 is greater than 1/5, even though 5 is greater than 2. When you make each number in its own denominator, it flips the inequality.
I'm gonna say it U DID IT BETTER THAN MY TEACHER
Carrying me since high school and college
this is my goat right here brother
Thank you for making videos.
Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on the Direct Comparison Test in Calculus Two. This topic in Calculus Two can be problematic, however students must know the different tests and how to apply them in different cases. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
11:50 could you use the integral series test for this?
Thanks God for your existence Doctor 💕
Thanks Jesus Christ 🙏
Here you are saving me again
Thank you again for your help! So damn easy to understand
Amazing video 🙂
This was very helpful
Question: "IN THIS VIDEO," if a sub n is inconclusive, do we leave the answer like that? Do we have to solve further to find if a sub n ("an") is divergent t or convergent?
Super explanation sir
You can also cross multiply an and bn to check which is bigger/smaller. Hope it helps someone.
why would you do that? isn't it obviously already that 1/(n+1) is smaller than 1/n?
@@凛-r3hsometimes its not obvious on harder questions
at 12:00 why did ln(n) have to be greater than 1? how did you know to do that?
You can refer to the graph of ln x
so helpful thank you once again !
In the problem 1/4+ n^1/3 , can't I use 1/n for comparison? 1/n < 1/4+n^1/3. Since 1/n diverges, then 1/4+n^1/3 diverges.
Correct me if I'm wrong
subscribed! thanks!
Thank you thank you thank you 😍
Thank you Dr.
I understood what was going on after the first example…compared to being almost lost in the sauce in a an hour lecture lol
Thanks a lot sir ❤
after watching your video , I hate my maths professor.
You have helped me alot
If bigger series diverges we cannot conclude the behavior of smaller series, why is it so?
I don't quite understand how it works in the case of a decreasing series. If bn is larger than an, but both are decreasing then how does bn converging tell us that an also does
this is the only reason i am passing calc 2