Convergence and Divergence - Introduction to Series

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/pHTCeohnft-tiZY

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Hallelujah

[@EldenEngineer]

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.

[@Carrymejane]

Huh it's calc 2? 😮

[@EldenEngineer]

@@Carrymejane what do you mean?

[@mondotrombo7167]

im learning this in precalc rn @@EldenEngineer

[@imCyanne]

@@EldenEngineer For some of us, this is calc 3 material

[@EldenEngineer]

@@imCyanne That's cool

[@tommydennen9563]

God I wish all teachers could make content as confident and straightforward as you are able to do. thank you!

[@sticraft41]

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.

[@KC-nn7kr]

could you explain to me if you got it i am still confused i have an exam soon

[@sticraft41]

​@KC-nn7kr The sequence is just the string of terms. The a_n =... is the 'code' that dictates what value each n term will have. Series is the sum of every term up to n: Σ_n= a_1 + a_2 +...a_n The sequence may converge, meaning that when heading to infinity, it effectively equals a certain number, eg. a_2 = 2.3, a_6 = 2.1, a_n = 2. That number could be anything, even zero. The series converges when all additional terms you add are effectively zero, thus not changing the value. If the sequence converges to a number =/= 0, for example 2, the series will diverge, because you'll be infinitely adding +2, never getting a set number. eg. Σ_4 = 8, Σ_5 = 10, Σ_100 = 200, Σ_n = infinity Hope this helps, I passed my exam, good luck to you too 👍🎉

[@Altair4611]

Knowing the difference between series and sequence is crucial

[@hsienkangliu1436]

yeah the 13:14 stuff confused me for a while

[@maalikserebryakov]

Thats like saying knowing the difference between definite integrals and functions is crucial…well yes? Its important to know what words mean. 🤓🤓🤓

[@user-fh2rw9zh8g]

What's the difference?

[@luisdmarinborgos9497]

And the sequence of partial sums

[@The_Average_Ragebait_Borutard]

@@maalikserebryakovDude, long time no see. Also, Base Boruto > All of Shippuden. 😂💪

[@georgesadler7830]

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 KZbin TV with the Organic Chemistry Tutor.

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Bruh how tf u doing this in college when I'm doing this shit in highschool

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@@var1232 😂 different syllabus I guess we did basics of this in high school 😂 now it's more advanced

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[@ProfessionalGasLighting]

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!

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negawatt isnt this precalc

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Ur watching calc vids for fun?

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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.

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Shame on the guy who disliked in the first 30 seconds

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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

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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.

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[@ashwinkotha3388]

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.

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[@prathikkannan3324]

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.

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Helped me understand in less than 20 mintues while my professor couldnt in over an hour. Thank You!!!

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The topics became easy when you teach ..So please make video related to line integral and Green's Theorem. Thank youu.

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[@smitad7881]

A huge thank you. This was confusing before I chanced upon your video.

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This is so cool! Great explanation, man.

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Finally understanding what is the meaning of converge and diverge lol

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Once again, thank you! Your videos have helped me maintain an A in calc II

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You just saved me, thank you so much

[@nicholasdupont2468]

12:20 Why do we multiply the top and bottom by 1/n?

[@BomBom-lo1pq]

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)

[@vincentmanning1338]

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

[@mrJackisnothere]

​@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 😂

[@HenriettaPritchard]

you make maths seem so easy! thank you :)

[@nicolejones3686]

Thanks for your help 😊

[@Elicruz2]

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.

[@xinpingdonohoe3978]

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.

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Great explanation☺

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Helped a lot thanks so much

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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. ❤

[@nyunai298]

Thanks. More convergence tests on series an sequences please

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You are best teacher in the world I respect you so much more. if you have time help me with hydraulic course

[@waleedo6178]

in 12:08, do we always multiply the equation with 1/n?? if someone knows why we used 1/n please reply

[@diegofernandez9078]

did you figured out why? asking the same question

[@Hey.i0]

me 3 i got stuck there

[@m1sterpinky]

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.

[@shinefake48]

He did that to cancel out the n in the equations, that way you can end up with some number +/- zero. thus ending up with the limit it is recommended when the top and bottom has variable to some power, its the same way that you would find the limit in calc 1

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[@kabirsethi2608]

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....

[@xinpingdonohoe3978]

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.

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amazing vid, made a lot of sense 😁

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Awesome explanation 💯

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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

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[@teamstudent4555]

13.15 L'Hopital rule also yields the same result:5/7

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Studying this for my exam. - Nieto, Desiree Ann B. BSECE 2B

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Helpful video thank you 🙏

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Please, make more videos on Series

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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

[@diegofernandez9078]

does anyone know why did he applied the 1/n on 12:45 ?

[@bm8524]

if you ever figure it out pls let me know I'm so lost on that

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Great content

[@doniasayari9936]

thank you so much

[@kristoffcolinayo9713]

I don't know if you answer comments but why did you multiply the a sub n by 1/n during the second example?

[@anelisriano9203]

Why did you multiple the top and bottom by 1/n?

[@venj251]

he multiplied the top and bottom by 1/n to evaluate the limit. If you just plugged in infinity for n it would be inf/inf so you have to algebraically manipulate the expression. could also use L’hopitals and come up with the same answer

[@srisources223]

Thanks, this really helped me.

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Bro you havent even watched this😑🤣🤣

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@@hamzazahidi5404 Yeah, Series-ly

[@srisources223]

@@hamzazahidi5404 I know, this is what I needed help with.

[@srisources223]

@@hamzazahidi5404 I worded it differently

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@@srisources223 It was you from the future after having watched the video comming back to the present to thank the channel and post an early comment too.

[@mosesmuturi1694]

I know you are here because your exams or cats are near,,I wish you all the best

[@nemanjalazarevic9249]

For 1:14 I noticed a formula: S(n)=n(n+1)

[@nyambayartogtohtur1525]

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?

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i love u guys fr life saver : )

[@ethioupdatedinfo.]

Hi

[@noahmaxario1448]

how did we find the general formula, and how many types of sequences are out there if it's fixed formula

[@sassy_o_sushi6304]

Can someone explain me why in 12:16 he divided the numerator and denominator with 1/n please 😢

[@nrnrlola7157]

It's so he can cancel out n . If he kept the n and put infinity, it wouldn't be correct

[@sassy_o_sushi6304]

@nrnrlola7157 thanks😅. I saw it with time🥲

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Do you have an email address. How do you follow your films in order. From beginning of math up to calculus

[@SISKCERTWaJaVlogs]

13:04 or maybe you can just do the lhopital to find the limit