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Convergence and Divergence: The Return of Sequences and Series

Professor Dave Explains
2018 ж. 14 Мау.
284 935 Рет қаралды
Жүктеу

We learned a little bit about sequences and series earlier in the mathematics course, but now its time to work with these some more, now that we understand calculus! First up, what does it mean for a sequence or series to be convergent or divergent, and how can we tell which one it is? Let's find out!
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EMAIL► ProfessorDaveExplains@gmail.com
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Пікірлер

  • Your voice is so clear and stress-relievingly good to hear.

    @emmaell6659@emmaell66593 жыл бұрын

  • Professor Dave I just came across your video and I want to express my appreciation at the very clear presentation of the concepts; not only are the slides very clear, you speak with a certain clarity which is rare to come by in a mathematics tutorial. Thank you .

    @mainulislam6765@mainulislam67653 жыл бұрын

  • Just the type of explanation I was looking for. Perfectly explained.

    @samitkumar1170@samitkumar11702 жыл бұрын

  • This man can explain a 3 month university subject in 10 Minutes

    @geektoys370@geektoys3707 ай бұрын

  • PROFESSOR you explained it so beautifully. Thanks.

    @harismasoom6634@harismasoom66342 жыл бұрын

  • Thank you for giving that example! I would love to see some more as you continue to do these videos

    @AnAzsproduction@AnAzsproduction5 жыл бұрын

  • I had a problem all during my semester in this concept.. but now it's so clear ! I can't thank u more man :)

    @saeedahmed-9290@saeedahmed-9290 Жыл бұрын

    • ​@@jonathanlimjun6238 what do you know about convergence

      @calculus8399@calculus8399 Жыл бұрын

  • Thanks for the video. This has made me understand a lot of things I have been missing. Good work!

    @katunduchabala7266@katunduchabala72662 жыл бұрын

  • Thanks professor Daves. This video really helped me in understanding the basics of convergent and divergent series. And , I would also like to place a demand for a video on Maclaurain's series.

    @debajyotisarkar1145@debajyotisarkar11453 жыл бұрын

    • I did that too, check the mathematics playlist!

      @ProfessorDaveExplains@ProfessorDaveExplains3 жыл бұрын

  • Thankyou sir for such a simplified explanation.

    @riyabiswas906@riyabiswas9064 жыл бұрын

  • Great video! your explanation is very easy to understand

    @chaosend3815@chaosend38155 жыл бұрын

  • Very good explanation. Thank you so much for all your nice demonstration.

    @jawwadshahed@jawwadshahed3 жыл бұрын

  • Thank you for this video, it has lifted up some uncertainties.

    @annaV513@annaV513 Жыл бұрын

  • thanks, man!! really clear and useful, and also insightful; ❤️❤️

    @AlessandroZir@AlessandroZir Жыл бұрын

  • Thanks for the knowledge you have shared with me.

    @douglasposho9299@douglasposho92993 жыл бұрын

  • you gotta do more of these man

    @TheBluePhoenix008@TheBluePhoenix00820 күн бұрын

  • at 8:50 why that sum will be divergent ? i thought it will converge to 1/5?

    @mathew_pang@mathew_pang2 жыл бұрын

    • same here

      @IslamicLifestylevibess@IslamicLifestylevibess2 жыл бұрын

  • thank you very much sir....this concept is clear to me now

    @nelayapu5789@nelayapu57894 жыл бұрын

  • It was a good revision! Great job 👏

    @nnofficial2414@nnofficial241416 күн бұрын

  • Very clear explanation, thanks!

    @niekbeijloos8355@niekbeijloos835510 ай бұрын

  • Perfectly explainedd🔥

    @zeinebkefeya1946@zeinebkefeya1946 Жыл бұрын

  • Crystal clear! Thank you!

    @johnholme783@johnholme7832 ай бұрын

  • Thank you so much.really helpful

    @niaala@niaala4 жыл бұрын

  • i like everything in the way how you explain!

    @nononnomonohjghdgdshrsrhsjgd@nononnomonohjghdgdshrsrhsjgd2 жыл бұрын

  • GREAT WORK KEEP UP!

    @irfankadem3628@irfankadem36282 жыл бұрын

  • Great explanation !

    @MissOk777@MissOk777 Жыл бұрын

  • Omg, thank you so much. This video really helped bridge the gap between all this information and how it works together. Before, it was like a jumbled mess in my head.

    @Sarah-re7cg@Sarah-re7cg2 жыл бұрын

    • @@jonathanlimjun6238 yeah, professor Dave is really great at explaining topics in a much more coherent and intuitive way

      @Sarah-re7cg@Sarah-re7cg Жыл бұрын

  • Thanks so much 🙏🏼🙏🏼🙏🏼I have understood a lot 😊

    @reengaesh7545@reengaesh75454 жыл бұрын

  • Excellent explanation

    @user-nw5uu2hu7w@user-nw5uu2hu7w2 жыл бұрын

  • Thaaaaanks a lot🙏Finally,I understood!

    @MimiMimi-ss7jk@MimiMimi-ss7jk3 жыл бұрын

  • Thanks loved it.

    @sidharthmohanty6434@sidharthmohanty64344 жыл бұрын

  • You are very helpful 😄😄❤️....

    @nabanitagoswami6652@nabanitagoswami66525 жыл бұрын

  • Thank you so much!!!

    @samjames1253@samjames12533 жыл бұрын

  • you're a goat for this video bro, respect g

    @antonioochoa2673@antonioochoa26736 ай бұрын

  • Like your animations

    @ericard4165@ericard41656 жыл бұрын

  • great lecture! Thank you professor a lot!

    @hailabseyoum5746@hailabseyoum5746 Жыл бұрын

    • @@jonathanlimjun6238 Nice bot

      @angadthandi2281@angadthandi2281 Жыл бұрын

  • Very very helpful!!!!! Thanks!!!!!!

    @user-cr8bd9qk1r@user-cr8bd9qk1r5 жыл бұрын

  • Thank you 🙏🙏🙏

    @fishlasagna7368@fishlasagna73685 жыл бұрын

  • THANK YOU SO MUCH

    @JoanKemon@JoanKemon Жыл бұрын

  • This helped me with my Alevel

    @danielgilder8672@danielgilder86723 жыл бұрын

  • Wow ....its all coming back to me!!

    @curtpiazza1688@curtpiazza16882 жыл бұрын

  • How can math be amazing like this 😍

    @Has_Chemist2.0@Has_Chemist2.09 ай бұрын

  • Then series diverge when they sum constants and ever increasing values and converge when they sum ever decreasing values? really simple and good explanation!

    @GodbornNoven@GodbornNoven2 жыл бұрын

  • This professor is good. I like this video

    @vianekabanda8348@vianekabanda8348 Жыл бұрын

  • Thank you Lord Farquad you are the best!

    @Oscar-gx2yf@Oscar-gx2yf5 жыл бұрын

  • Thank you 😊👍 so much from India.

    @ECEAbhishekKumar@ECEAbhishekKumar3 жыл бұрын

  • so helpful

    @jamebello9869@jamebello98695 жыл бұрын

  • Thank.You Professor

    @nweniaung9621@nweniaung96212 жыл бұрын

  • "let's converge a little"

    @ClumpypooCP@ClumpypooCP6 жыл бұрын

    • Good one

      @juraijbinjamal5313@juraijbinjamal53134 жыл бұрын

    • converge me daddy UwU

      @f3ralp1g3on6@f3ralp1g3on63 жыл бұрын

    • @@f3ralp1g3on6 ayo- 🤨🤚

      @The-Cookie@The-Cookie2 жыл бұрын

  • Thank you

    @harrisonbennett7122@harrisonbennett71225 жыл бұрын

  • Pro Dave u are the best........................!!!!!!!!!!!!!

    @mahinduliyanage1583@mahinduliyanage15834 жыл бұрын

  • (6:35): for r=-1, the terms are a,-a, a,-a, a,-a… .

    @davideveringham3827@davideveringham38274 жыл бұрын

  • 0:50 bold of you to assume that 😅

    @pluto4301@pluto43013 жыл бұрын

  • He knows a lot about all kinds of stuff

    @noahgsolomon@noahgsolomon Жыл бұрын

  • thanks sir

    @sandeepanpoddercse3819@sandeepanpoddercse38192 жыл бұрын

  • Is it possible for a sequence with two different numbers to converge?

    @julytdalida4860@julytdalida48603 жыл бұрын

  • thank you

    @ishiitapal@ishiitapal3 жыл бұрын

  • great man

    @shahrukhkhanshahrukh3504@shahrukhkhanshahrukh35043 жыл бұрын

  • Hey Dave. Would you consider following up this course with a linear algebra course? All the best, Bram

    @TheBrammiej@TheBrammiej6 жыл бұрын

    • don't worry, linear algebra is coming! i already filmed some of it.

      @ProfessorDaveExplains@ProfessorDaveExplains6 жыл бұрын

    • Professor Dave Explains Hugs!

      @TheBrammiej@TheBrammiej6 жыл бұрын

  • When the limit of a sequence is zero then the corresponding series will be convergent and when the limit of a sequence gives some constant value L then the sequence is convergent. Is this right? Please correct me.

    @sachinrajpandey5242@sachinrajpandey52422 жыл бұрын

  • Ty for making me understand bro

    @raghavtandon8033@raghavtandon80335 жыл бұрын

  • Sir , limit of1/n is zero still series is divergent this theorem goes wrong in this case is it exception ??????? Pls reply sir

    @beetaff7841@beetaff7841 Жыл бұрын

  • 1:16 This seems like a divergent series but actually is convergent. There are some simple and complex proofs to show that 1+2+3+.....= -1/12. This is same as Riemann zeta function for -1.

    @supreethmv@supreethmv Жыл бұрын

  • so if the resulting series is zero it is convergent?

    @Ashish-hl7rk@Ashish-hl7rk Жыл бұрын

  • whats the name of the theorem at 7:17?

    @jontedeakin1986@jontedeakin19862 жыл бұрын

  • Hi prof Dave .do you have videos about Taylor and Mclaurin series.Thank you.

    @fernanmontevista204@fernanmontevista2042 жыл бұрын

    • Yep!

      @ProfessorDaveExplains@ProfessorDaveExplains2 жыл бұрын

  • love from India

    @courageandpeace1944@courageandpeace19445 жыл бұрын

  • Hey can a convergent sequence have an answer which is a complex number...as n approaches infinity

    @shankarabhat7505@shankarabhat75055 жыл бұрын

    • hmm yes i believe so, at least definitely if there are complex numbers in the sequence!

      @ProfessorDaveExplains@ProfessorDaveExplains5 жыл бұрын

  • 7:05 how to get that answer?

    @ckarcher4504@ckarcher45044 ай бұрын

  • This Math Is Worse Than Programming.... My Head Is About To Explode

    @GSNn@GSNn2 жыл бұрын

  • Hey professor Dave, what else after calculus in this course

    @ericard4165@ericard41655 жыл бұрын

    • linear algebra! and then hopefully differential equations.

      @ProfessorDaveExplains@ProfessorDaveExplains5 жыл бұрын

    • thanks they're really helpful

      @ericard4165@ericard41655 жыл бұрын

  • I don't get it because at the beginning he said that if it gets to a finite number it is convergent and in the end when he gets1/5 he said it is divergent ;-; please somebody help me

    @rinr3300@rinr33003 ай бұрын

  • Pirates if they give up Piracy and go to the Caribbean University 6:05

    @salaa23@salaa233 жыл бұрын

  • 🙏🏻 🙏🏻 🙏🏻

    @JillianRiccio-rv3nu@JillianRiccio-rv3nu7 күн бұрын

  • which playlist is this video in?????

    @user-xb8qh9qu1c@user-xb8qh9qu1c Жыл бұрын

    • math

      @ProfessorDaveExplains@ProfessorDaveExplains Жыл бұрын

  • 2:54 the sequences should start from 1

    @leejunzhao@leejunzhao Жыл бұрын

  • nice

    @cavendis3423@cavendis34235 жыл бұрын

  • I lost it at "In fact,..." 7:10 😪

    @thestar001Official@thestar001Official2 жыл бұрын

  • I needed help on precalc 20 and it started talking about integrals and limits 😥😥

    @joongi9839@joongi98394 жыл бұрын

    • i have a tutorial earlier in my mathematics playlist on sequences and series, that's probably the one you're looking for. just go to the long playlist, it's somewhere in the 80s i think.

      @ProfessorDaveExplains@ProfessorDaveExplains4 жыл бұрын

  • I confused how lim of 1/2^n = 1 . I thought it should be 0. becz 1/inf = 0.

    @sedeqalsakkf9315@sedeqalsakkf93153 жыл бұрын

    • he just said in the video clearly that if a sequence converges to 0 as it approaches its infinite-th term, the series that the sequence generates would have a finite number limite. i think u're mixing up sequence and series, which is the first thing he stated in the video

      @RickyRicheRebelle@RickyRicheRebelle3 жыл бұрын

  • 2:17 Why Am I laughing so hard

    @imbreakingdown2683@imbreakingdown26832 жыл бұрын

  • 🙏

    @koamivikeledome9713@koamivikeledome9713 Жыл бұрын

  • ❤

    @hammadullahshaikh4735@hammadullahshaikh4735 Жыл бұрын

  • If you are going to reference previous tutorials, a link in the comments would be good.

    @wjrasmussen666@wjrasmussen6663 жыл бұрын

    • just go to my mathematics playlist, also i usually link using cards in the top right

      @ProfessorDaveExplains@ProfessorDaveExplains3 жыл бұрын

  • First equation = -1/12 ;)

    @ccbgaming6994@ccbgaming69942 жыл бұрын

  • 来自华东地区某211高校，看完这个视频才知道国内高数老师是什么东西😅

    @murphy6177@murphy6177 Жыл бұрын

  • 4:37 .1+2+3+....=-1/12 ...ramanujuan....

    @sanjaycosmos9679@sanjaycosmos96794 жыл бұрын

    • It is a special case for a special type of function. You will get zero no. If you write this in your exam

      @SurajSharma-pv3di@SurajSharma-pv3di4 жыл бұрын

    • Only using analytic continuation on a different function (continued riemman zeta function) that is closely related to but not interchangeable with that sum. The function that gives you that sum (riemman zeta function) only works for inputs with a real part greatrr than one. The RZ function breaks when you get smaller than one. But if you "continue" the riemman zeta function throughout the complex plane (ensuring it is analytically continued), when you plug in (-1), which using the non-continued riemman zeta function (∑«n=1→∞» (1/n^s) for varying values of s) would blow up to infinity, you get (-1/12). So there is a sense in which the sum you get from the non continued RZ function, 1+2+3+4... also equals (-1/12).

      @scptime1188@scptime11882 жыл бұрын

  • Simple af

    @PratimMukherjee@PratimMukherjee3 жыл бұрын

  • I'm here from FLVS (Florida Virtual School) and I would like to say Big Chungus Funny.

    @adventuresofgaara8936@adventuresofgaara89363 жыл бұрын

  • 1+2+3+4+5+……= -1/12 😢

    @badreddineadrham9605@badreddineadrham9605 Жыл бұрын

  • ❤❤❤❤❤❤❤❤❤❤❤

    @Diviner-ip2pq@Diviner-ip2pq9 ай бұрын

  • Sir still I haven't got a reply. Waiting for your explanation. Creating a youtube clip for those questions will be realy helpful. Waiting for your email

    @gaminisiriwardana5946@gaminisiriwardana59464 жыл бұрын

  • wasn't it -1/12

    @gautamchettiar4150@gautamchettiar41504 жыл бұрын

    • The sum of all *n* natural numbers is a diverging series coz it doesn't approach any sensible value , try substituting as n→∞ in the formula n(n+1)/2 , -1/12 isn't the true sum coz this result can't be verified using the convergence and divergence test!

      @wolframalpha8634@wolframalpha86344 жыл бұрын

    • @@wolframalpha8634 the result can't be found as addition doesn't happen assuming a linear number line (well I know line is linear , dunno how else to put it in words) . And also he did put n as infinite and write sum as infinite so.... Btw thx

      @gautamchettiar4150@gautamchettiar41504 жыл бұрын

    • @@gautamchettiar4150 uhmm.. I didn't understand about addition on a linear number line?

      @wolframalpha8634@wolframalpha86344 жыл бұрын

    • @@wolframalpha8634 you can understand it on 3b1b channel's video

      @gautamchettiar4150@gautamchettiar41504 жыл бұрын

    • @@gautamchettiar4150 thanks! I'll watch it

      @wolframalpha8634@wolframalpha86344 жыл бұрын

  • best

    @sehreenrani9608@sehreenrani96085 жыл бұрын

  • @Mr_Passionate@Mr_Passionate3 жыл бұрын

  • convergent = limit does not exist

    @umararshad9567@umararshad95672 жыл бұрын

  • 수학이랑 영어를 합하니 배로 좆같네;;

    @dareto2181@dareto21812 жыл бұрын

  • Jujutsu kaisen brought me here

    @adriaaan.n@adriaaan.n2 жыл бұрын

  • this video has false information,a limit of a sequence can exist and be equal to a real number and the sequence can diverge.

    @darknightcorexd7227@darknightcorexd72275 жыл бұрын

    • if a sequence converges at some finite number, it's convergent. that's what "converge" means. a divergent sequence goes to infinity, by definition.

      @ProfessorDaveExplains@ProfessorDaveExplains5 жыл бұрын

  • Its wrong, as the series n^2/(5n^2+4) would be a convergent series.......please don't try to teach till you are not fully clear in your concept

    @codexsreyans9141@codexsreyans91415 жыл бұрын

    • It's a convergent sequence, but it does not converge to zero, so the series that is the sum of the terms of the corresponding sequence will be divergent. Please don't try to make presumptuous comments until you are fully clear on the concepts.

      @ProfessorDaveExplains@ProfessorDaveExplains5 жыл бұрын

    • You should first understand the relation between a SEQUENCE and a SERIES before making presumptuous comments...

      @johnoconnor2648@johnoconnor26485 жыл бұрын
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