Convergence and Divergence - Introduction to Series
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- Опубліковано 19 січ 2021
- This calculus 2 video tutorial provides a basic introduction into series. It explains how to determine the convergence and divergence of a series. It explains the difference between a sequence and a series. This video includes examples and practice problems with geometric series, harmonic series, and the telescoping series. It also discusses the divergence test.
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the lord has provided us once more
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God I wish all teachers could make content as confident and straightforward as you are able to do. thank you!
You helped me pass Calc II in 8 weeks this summer with a 90 on my final and a 90 as my grade. I got a 96 in Calc I before that with your help. Now I have Calc III this fall and I’m thinking I’m gonna be doing better than this past summer. Thank you so much OCT!
Hows Calc 3 compared to Calc 2?
@@andrean40 my school is a little weird and has Calc split into 4 parts. Our 3 consists mostly of series and sequences. After Taylor series it moved to 3D graphs and functions. From here I’m not sure what’s next. But in 4 I know it focuses all on multi variable calculus. So I guess 3 will stop right before that. Hopefully this makes sense and is helpful.
Awww I'm so proud of you
Knowing the difference between series and sequence is crucial
yeah the 13:14 stuff confused me for a while
Thats like saying knowing the difference between definite integrals and functions is crucial…well yes?
Its important to know what words mean. 🤓🤓🤓
What's the difference?
And the sequence of partial sums
A lot of my early confusion with this section of calc 2 is just vocab and over complicated notation. Thanks for helping me get that stuff straight. It starts to make sense with time and rewatching these videos.
Huh it's calc 2? 😮
@@Carrymejane what do you mean?
im learning this in precalc rn @@EldenEngineer
@@EldenEngineer For some of us, this is calc 3 material
@@imCyanne That's cool
Professor Organic Chemistry Tutor, thank you once again for another fantastic video/lecture on Convergence and Divergence of a Series in Calculus Two. This is a large topic in Calculus and students will have problems with understanding these concepts. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
I love all your videos! I would definitely love to see more of these Calc and Calc 2 videos! I’m currently in Calc 2 and seeing how you work through different examples definitely helps me learn how to apply those thought processes to my own problems! But I definitely need more series and sequence videos! Even if they’re just working through more complicated examples so I know how to use the limit comparison test to a p series and how to know which test to use etc!
negawatt isnt this precalc
Shame on the guy who disliked in the first 30 seconds
It was a tenured professor who doesn't like how his students prefer this guy's videos to his dull lectures in which he narrates the chapters from Cenage.
Meanwhile I 👍 the vid before it even starts .... coz you already know that the explanation would be simple enough to understand 😁😁😁
I don't see any dislike on this video. But if what you're saying is true, then whoever disliked this video probably didn't like long form content. Because he has the attention span of a goldfish
@@joeyGalileoHottolol
Finishing Calc 2 right now and your videos have helped so much. I especially appreciate the emphasis on the difference between the finite sequence and the infinite series in the last couple problems.
Sir Julio Gonzales thanks for the help you offer us , this showed up on my F.maths test and i hit it real bad.. Your such help to me since high school .. Hope to meet you someday.
Ohh my goddd just finished this topic in college and needed this so much😭😁😁😁
Our god loves you 🌟❤️
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Bruh how tf u doing this in college when I'm doing this shit in highschool
@@var1232 😂 different syllabus I guess we did basics of this in high school 😂 now it's more advanced
@@sarah.moh22 please stop being cringe
Perfect timing as I needed to review these
Early too iam subscribed to this channel and I do not even study any of these just like the channel it's very good😀
Ur watching calc vids for fun?
Not me tryna understand Gojo's limitless
WE!
This is so cool! Great explanation, man.
i go to berkeley and half the class learns from this dude instead of the lecturers 💀
Best presentations in mathematics ever 'no joke' ,great videos, keep it up sir...
The topics became easy when you teach ..So please make video related to line integral and Green's Theorem. Thank youu.
Once again, thank you! Your videos have helped me maintain an A in calc II
So many years back, I studied it in my college days. For Maths. lovers it is interesting. But I found it is equally interesting even for a layman for the way you are teaching. Thank you for explaining the basic concept of limit and infinity in a simple way.
I can smell the Poop from your comment
Take the Poo to the Loo! 💩💩💩💩💩
You teach almost flawlessly well
God bless u bruv
Wow, everything is clear.
Thanks Sir
I just hope you never quit UA-cam
youre a hero for saving all these people's grades!!! tysm!
Thanks. More convergence tests on series an sequences please
A huge thank you. This was confusing before I chanced upon your video.
Thank you sir 🤪
Loving it💯💯
you make maths seem so easy! thank you :)
My instructor waited until after withdrawal date to totally drop the ball on teaching. Thanks for this
Awesome explanation 💯
Brother, you have saved my mental health. TY :D
man is there anything that you dont have a video on? at this stage im going to get an engineering degree from the organic chemistry tutor university not from my actual uni. you saved me many times and i thank you every time. YOU ARE THE BEST!!!
Hello
thank you very much sirr!! i cant focus during the whole week of this chapter bcs of test of other subjects... but u saved me!!!
Helped a lot thanks so much
Awesome! thank you soo much for this lecture.
Helpful video thank you 🙏
amazing vid, made a lot of sense
😁
thank you so much
This guy has videos of almost every mathematical concept on earth
Thank you. Your video teach me well.🙏👍
This is great 💯
Thank you sir
Bro Saving me from the traps of Calculus! Thank You.
Fantastic work keep it up
You're the teaching GOAT
really saved me with this one, prof.
i need more calc2 videos to stay afloat, plss :'D
You just saved me, thank you so much
i really donot know with what word must i express my great respect and thanks for you.you are real mathematician
Egziabeher Ymassgan
Thanks JG!
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He's been saving my gpa for like 3 years
this guy is always posting vids of a topic while im ttaking the same topic
You are best teacher in the world I respect you so much more. if you have time help me with hydraulic course
Thanks for your help 😊
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I wouldn't be surprised if a Harvard prof. recommends this channel to the students.
Na not rly, This is just a very non-rigorous application of series. His videos are generally just teaching rules to memorize, rather than shedding intuition and light. No hate against him, he is still helping loads of people, but at a Harvard level u would be rly concerned about making this stuff rly rigorous.
thank you very much!
Hey JG could you post some videos sin regards to Laplace transform (diffriential equations)? Your EE sections are so helpful, I am struggling to get this concept and was hoping you'd make a section sometime in the future! Either way I appreciate what you're doing to help normalize STEM studies, and its been a great experience learning from you
All the best
MP
Helped me understand in less than 20 mintues while my professor couldnt in over an hour. Thank You!!!
I don't know if you answer comments but why did you multiply the a sub n by 1/n during the second example?
Hi thanks for your video I have a question, can you just multiply by 1/n in limit isnt it just like multiplying any fractional number by 0/0 and telling that any fractional number is equal to 0?
thank you so much!
this was uploaded on my b-day :D
the Organic Chemistry tutor saving my calculus grade
Finally understanding what is the meaning of converge and diverge lol
Please, make more videos on Series
Me before watching this video: I dont get shit about when a series converges
Me after watching this video: ... Thats it? THATS IT?!
seriously, your explainations are so damn good. You're my savior
Thanks!
Just asking,
As per Ramanujan Summation, 1+2+3+4+.. all the way up to infinity is -1/12. Therefore on multiplying both sides we get,
2+4+6+....=-1/6.
So shouldn't the answer for the first series be -1/6.
If any mistakes please correct me as I am just learning....
Ramanujan Summation is a method of applying conversant results to divergent answers, like an integral having a Cauchy Principle Value. The actual thing diverges, but -1/12 is what arises if you do the series in other branches of mathematics.
In regular maths though, it diverges.
Do you have an email address. How do you follow your films in order. From beginning of math up to calculus
The problem I was looking for is advertised on the youtube search in this video but here its accessible only on patreon. First time this guy has let me down.
Your explain is perfect. Thank-you soo much. This is better
Thank you king
how did we find the general formula, and how many types of sequences are out there if it's fixed formula
thank you legend
13:08 is exactly what I needed to hear. I was confused and thought that in converged because it had a finite number but that's only for the sequence.
If the limit at ∞ doesn't equal 0, like here it equals 5/7, then the series is going to be around ∞×5/7, because after while an≈5/7, and there are still an infinite number of terms left.
Only ∞×0 is not always going to diverge, which is why the limit at ∞ must be 0.
Thank you
00:01 Learn how to determine if a series converges or diverges
02:05 Determining if a series converges or diverges
04:19 Determining convergence or divergence of infinite series
06:15 The series diverges
08:20 The divergence test is a quick way to determine if a series diverges or not.
10:26 The series is divergent using the divergence test.
12:36 The series diverges according to the divergence test.
14:29 For a series to converge, the limit as n approaches infinity for a sub n must be equal to zero.
Crafted by Merlin AI.
i love u guys fr life saver : )
Hi
I am emailing this to my prof.
I found this helpful, also...I love you.
13.15 L'Hopital rule also yields the same result:5/7
I don't understand the limits can you please explain and how to plot it in calcu?
why we use divergent test for?
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I don't understand
Here you said if a series has a value then it converges but in n th term divergence test in your other video if it has a value different from zero then it diverges.
I don't get it please explain 🤧
12:20 Why do we multiply the top and bottom by 1/n?
These are the steps you have to follow when trying to find the limit of a function as the variable approaches infinity.
You divide both the numerator and denominator by the highest power of the variable found in the denominator.
For example, if you’re trying to find the limit when x approaches zero for:
2x^3 +5/6x
You will divide both the numerator and denominator by x (or multiply both by 1/x)
This is okay here but in general it is probably better to use L’Hopital’s rule when dealing with limits of indeterminate form such as 0/0 or inf/inf. Simply take the derivative of the numerator and the derivative of the denominator and compute the limit as n approaches inf of the new function. Repeat as necessary
@vincentmanning1338 thank you for this, I find the other option difficult to apply (it doesn't come natural for me) so knowing I can also do it the other way gives me some peace of mind 😂
GOD BLESS YOU MAN
Make videos on divergence, Stokes', greens theorem
God, well wish me good luck people. I’m gonna be reviewing these videos cause I’m at a 66 and got my Calc 2 final in 2 weeks. ❤
you help me so much through math
Why did you multiply by 1/n
In this equation of 5n+3/7n-4
I love this topic
how did you determain the terms in 5:52 ?
You are legend
convergese sequence have finite value or equals to zero. so in second ? 5/7 is finite value and you say it divergense
help me with this doubt
It diverges by the nth term test. As the terms approach infinity, the value goes to 5/7 which gets added an infinite number of times, this it is infinite and diverges.
thanks
I really do enjoy these videos and has truly helped a lot. But because of your accent sometimes it is tough for me as a non-native English speaker to understand what you are trying to convey.
i do wish you were my college maths professor.