Convergence and Divergence - Introduction to Series
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- Опубликовано: 6 сен 2024
- 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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amen
YHWH we love to shout your name o’lord.
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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
Cool, I have all that (except multivariable and double integrals) in one subject + theory (real analysis). I am cooked...
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
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
This is the most important and clarifying point I believe, at 13:05 when you state that the sequence converges, but the series diverges. Thank you for these videos and explanations.
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?
Ohh my goddd just finished this topic in college and needed this so much😭😁😁😁
Our god loves you 🌟❤️
@@sarah.moh22 jesus is king💯
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
Not me tryna understand Gojo's limitless
WE!
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
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 RUclips TV with the Organic Chemistry Tutor.
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.
I just hope you never quit RUclips
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
i go to berkeley and half the class learns from this dude instead of the lecturers 💀
youre a hero for saving all these people's grades!!! tysm!
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.
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! 💩💩💩💩💩
The topics became easy when you teach ..So please make video related to line integral and Green's Theorem. Thank youu.
Best presentations in mathematics ever 'no joke' ,great videos, keep it up sir...
Brother, you have saved my mental health. TY :D
i really donot know with what word must i express my great respect and thanks for you.you are real mathematician
Egziabeher Ymassgan
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
Perfect timing as I needed to review these
Bro Saving me from the traps of Calculus! Thank You.
Thanks!
This guy has videos of almost every mathematical concept on earth
He's been saving my gpa for like 3 years
You're the teaching GOAT
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.
Helped me understand in less than 20 mintues while my professor couldnt in over an hour. Thank You!!!
Finally understanding what is the meaning of converge and diverge lol
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 😂
OUR SALVATION HAS BEEN BESTOWED UPON US ONCE AGAIN FROM THE GREAT HEAVENS
This is so cool! Great explanation, man.
this guy is always posting vids of a topic while im ttaking the same topic
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.
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.
You teach almost flawlessly well
God bless u bruv
Once again, thank you! Your videos have helped me maintain an A in calc II
A huge thank you. This was confusing before I chanced upon your video.
I found this helpful, also...I love you.
My instructor waited until after withdrawal date to totally drop the ball on teaching. Thanks for this
Your explain is perfect. Thank-you soo much. This is better
really saved me with this one, prof.
I am emailing this to my prof.
Wow, everything is clear.
Thanks Sir
how did we find the general formula, and how many types of sequences are out there if it's fixed formula
You are best teacher in the world I respect you so much more. if you have time help me with hydraulic course
the Organic Chemistry tutor saving my calculus grade
I don't know if you answer comments but why did you multiply the a sub n by 1/n during the second example?
Every Time every....... Timeeeeeee
Thank You 🥺❤️
Thanks. More convergence tests on series an sequences please
you make maths seem so easy! thank you :)
Helped a lot thanks so much
Thanks for your help 😊
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!!!
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.
13.15 L'Hopital rule also yields the same result:5/7
You just saved me, thank you so much
this was uploaded on my b-day :D
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?
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.
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.
Please, make more videos on Series
Do you have an email address. How do you follow your films in order. From beginning of math up to calculus
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
Thank you. Your video teach me well.🙏👍
Thank you 🥹
i need more calc2 videos to stay afloat, plss :'D
This is great 💯
Thank you sir
Awesome explanation 💯
Why did you multiply by 1/n
In this equation of 5n+3/7n-4
does anyone know why did he applied the 1/n on 12:45 ?
if you ever figure it out pls let me know I'm so lost on that
i do wish you were my college maths professor.
thank you legend
in 12:08, do we always multiply the equation with 1/n?? if someone knows why we used 1/n please reply
did you figured out why? asking the same question
me 3 i got stuck there
Only in some cases, he's multiplying the top and bottom with (1/n) to create 0s in the equation, otherwise he would've gotten (5(∞)+3) / (7(∞)-4) = ∞/∞ which is undefined.
Awesome! thank you soo much for this lecture.
Thank you sir 🤪
Loving it💯💯
Thank you
You are my hero bro!!
thank you so much!
Fantastic work keep it up
amazing vid, made a lot of sense
😁
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. ❤
Helpful video thank you 🙏
i love u guys fr life saver : )
Hi
Studying this for my exam.
- Nieto, Desiree Ann B. BSECE 2B
CASIA, AXLE JADE D.
BS-ECE 2B
Thanks JG!
thanks
I don't understand the limits can you please explain and how to plot it in calcu?
GOD BLESS YOU MAN
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.
cant wait to just pass this class. i know calc 3 is easier, i mean calc isnt hard, but im taking a summer class so im grinding tf outta this class i just need a B. im taking 4 fucking classes FML
thank you so much
Villarin, Paul Patrick W.
BSECE 2B
why we use divergent test for?