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Convergence and Divergence - Introduction to Series

The Organic Chemistry Tutor
2021 ж. 19 Қаң.
1 082 725 Рет қаралды
Жүктеу

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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  • Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzhead.info/sun/oaeYeblpgKywhmw/bejne.html

    @TheOrganicChemistryTutor@TheOrganicChemistryTutor Жыл бұрын

  • the lord has provided us once more

    @bramkreulen3553@bramkreulen35533 жыл бұрын

    • Hallelujah

      @schuylerjones1099@schuylerjones1099 Жыл бұрын

    • amen

      @tanishpanjwani3117@tanishpanjwani3117 Жыл бұрын

    • YHWH we love to shout your name o’lord.

      @joshuwa.jeremiah229@joshuwa.jeremiah229 Жыл бұрын

    • 😂😂😂😂

      @odikaebenezer4504@odikaebenezer4504 Жыл бұрын

    • Hallelujah

      @user-ix3cv9bc3o@user-ix3cv9bc3o5 ай бұрын

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

    @tommydennen9563@tommydennen9563 Жыл бұрын

  • Knowing the difference between series and sequence is crucial

    @Altair4611@Altair46112 жыл бұрын

    • yeah the 13:14 stuff confused me for a while

      @hsienkangliu1436@hsienkangliu1436 Жыл бұрын

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

      @maalikserebryakov@maalikserebryakov11 ай бұрын

    • What's the difference?

      @user-fh2rw9zh8g@user-fh2rw9zh8g7 ай бұрын

    • And the sequence of partial sums

      @luisdmarinborgos9497@luisdmarinborgos94976 ай бұрын

  • 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.

    @jamesyanney4027@jamesyanney40279 ай бұрын

    • Huh it's calc 2? 😮

      @Carrymejane@Carrymejane2 ай бұрын

    • @@Carrymejane what do you mean?

      @jamesyanney4027@jamesyanney40272 ай бұрын

    • im learning this in precalc rn @@jamesyanney4027

      @mondotrombo7167@mondotrombo716724 күн бұрын

    • @@jamesyanney4027 For some of us, this is calc 3 material

      @imCyanne@imCyanne23 күн бұрын

    • @@imCyanne That's cool

      @jamesyanney4027@jamesyanney402723 күн бұрын

  • 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!

    @BigCatSoftware@BigCatSoftware7 ай бұрын

    • Hows Calc 3 compared to Calc 2?

      @andrean40@andrean405 ай бұрын

    • @@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.

      @BigCatSoftware@BigCatSoftware5 ай бұрын

    • Awww I'm so proud of you

      @angelmclemore1785@angelmclemore17852 ай бұрын

  • 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.

    @chrisp2639@chrisp26399 ай бұрын

  • 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!

    @Sthanisn@Sthanisn3 жыл бұрын

    • negawatt isnt this precalc

      @mondotrombo7167@mondotrombo716724 күн бұрын

  • Early too iam subscribed to this channel and I do not even study any of these just like the channel it's very good😀

    @xadanmi-llion8520@xadanmi-llion85203 жыл бұрын

    • Ur watching calc vids for fun?

      @joshuacabezas8061@joshuacabezas80612 жыл бұрын

  • Shame on the guy who disliked in the first 30 seconds

    @krupt5995@krupt59953 жыл бұрын

    • 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.

      @joeyGalileoHotto@joeyGalileoHotto3 жыл бұрын

    • Meanwhile I 👍 the vid before it even starts .... coz you already know that the explanation would be simple enough to understand 😁😁😁

      @jazz7829@jazz78292 жыл бұрын

    • 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

      @oentrepreneur@oentrepreneurАй бұрын

    • ​@@joeyGalileoHottolol

      @oentrepreneur@oentrepreneurАй бұрын

  • Ohh my goddd just finished this topic in college and needed this so much😭😁😁😁

    @yashisingh6085@yashisingh60853 жыл бұрын

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      @MALAK.alrhmat@MALAK.alrhmat3 жыл бұрын

    • @@MALAK.alrhmat jesus is king💯

      @Daniel-qy4di@Daniel-qy4di3 жыл бұрын

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

      @var1232@var12323 жыл бұрын

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

      @yashisingh6085@yashisingh60853 жыл бұрын

    • @@MALAK.alrhmat please stop being cringe

      @Luka_c123@Luka_c1232 жыл бұрын

  • 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 KZhead TV with the Organic Chemistry Tutor.

    @georgesadler7830@georgesadler78302 жыл бұрын

  • 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.

    @MichaelHoughton22@MichaelHoughton223 жыл бұрын

  • Perfect timing as I needed to review these

    @declancampbell848@declancampbell8483 жыл бұрын

  • Best presentations in mathematics ever 'no joke' ,great videos, keep it up sir...

    @lybittaye@lybittaye2 жыл бұрын

  • I just hope you never quit KZhead

    @mello-rl6418@mello-rl64183 жыл бұрын

  • This is so cool! Great explanation, man.

    @Idk-qb9mb@Idk-qb9mb Жыл бұрын

  • Wow, everything is clear. Thanks Sir

    @josephtetteh8493@josephtetteh8493 Жыл бұрын

  • You teach almost flawlessly well God bless u bruv

    @jnr_classy@jnr_classy2 жыл бұрын

  • youre a hero for saving all these people's grades!!! tysm!

    @andrewmorrissy3122@andrewmorrissy3122 Жыл бұрын

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

    @user-sp1of1ic3h@user-sp1of1ic3h6 ай бұрын

  • Thanks. More convergence tests on series an sequences please

    @nyunai298@nyunai2982 жыл бұрын

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

    @zerinfaaruqui1338@zerinfaaruqui1338 Жыл бұрын

  • 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.

    @prabhanjanbag5738@prabhanjanbag57382 жыл бұрын

    • I can smell the Poop from your comment Take the Poo to the Loo! 💩💩💩💩💩

      @maalikserebryakov@maalikserebryakov11 ай бұрын

  • you make maths seem so easy! thank you :)

    @HenriettaPritchard@HenriettaPritchard2 жыл бұрын

  • Awesome explanation 💯

    @abd......@abd......2 жыл бұрын

  • Brother, you have saved my mental health. TY :D

    @user-ig9yz9wx8w@user-ig9yz9wx8w11 ай бұрын

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

    @smitad7881@smitad78814 ай бұрын

  • This is great 💯 Thank you sir

    @mutuginjokiwinnie@mutuginjokiwinnie8 ай бұрын

  • Thank you sir 🤪 Loving it💯💯

    @ilovefootball6975@ilovefootball69753 жыл бұрын

  • My instructor waited until after withdrawal date to totally drop the ball on teaching. Thanks for this

    @Agawin007@Agawin0072 жыл бұрын

  • 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!!!

    @nurul5971@nurul59713 жыл бұрын

  • Helped a lot thanks so much

    @volvelily3656@volvelily36563 жыл бұрын

  • Awesome! thank you soo much for this lecture.

    @amritheshk7151@amritheshk71513 жыл бұрын

  • Fantastic work keep it up

    @francislekula5590@francislekula5590 Жыл бұрын

  • Thank you. Your video teach me well.🙏👍

    @latihankalkulus@latihankalkulus Жыл бұрын

  • Helpful video thank you 🙏

    @breadstick4443@breadstick44433 жыл бұрын

  • amazing vid, made a lot of sense 😁

    @thejtblckwngs@thejtblckwngs Жыл бұрын

  • This guy has videos of almost every mathematical concept on earth

    @renukanandini9401@renukanandini9401 Жыл бұрын

  • Every Time every....... Timeeeeeee Thank You 🥺❤️

    @Muhammad_Waleed@Muhammad_Waleed Жыл бұрын

  • You just saved me, thank you so much

    @dabeeramir1407@dabeeramir14075 ай бұрын

  • i go to berkeley and half the class learns from this dude instead of the lecturers 💀

    @64_bit80@64_bit802 жыл бұрын

  • He's been saving my gpa for like 3 years

    @seanm323@seanm323 Жыл бұрын

  • thank you so much

    @doniasayari9936@doniasayari99362 жыл бұрын

  • this guy is always posting vids of a topic while im ttaking the same topic

    @zeyad7947@zeyad79473 жыл бұрын

  • i really donot know with what word must i express my great respect and thanks for you.you are real mathematician

    @user-ge5qy3ek9f@user-ge5qy3ek9f2 жыл бұрын

    • Egziabeher Ymassgan

      @zaracampbell6091@zaracampbell6091 Жыл бұрын

  • Thanks for your help 😊

    @nicolejones3686@nicolejones36864 ай бұрын

  • ur doing gods work and i love u

    @michellemariewidelski2522@michellemariewidelski25222 жыл бұрын

  • 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!!!

    @batata5T@batata5T2 жыл бұрын

    • Hello

      @Filmyworld.999@Filmyworld.9999 ай бұрын

  • You are my hero bro!!

    @coleschaeffer2293@coleschaeffer22932 жыл бұрын

  • Thanks JG!

    @GJRahul-vq6uu@GJRahul-vq6uu3 жыл бұрын

  • the Organic Chemistry tutor saving my calculus grade

    @LinY-vs4dv@LinY-vs4dv Жыл бұрын

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

    @samiabegum4607@samiabegum46072 жыл бұрын

  • 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

    @gravkint8376@gravkint83762 жыл бұрын

  • 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

    @marcusperla6837@marcusperla68373 жыл бұрын

  • Your explain is perfect. Thank-you soo much. This is better

    @engisasp4808@engisasp48082 жыл бұрын

  • i need more calc2 videos to stay afloat, plss :'D

    @5am484@5am4843 жыл бұрын

  • I wouldn't be surprised if a Harvard prof. recommends this channel to the students.

    @Bugatti0wner@Bugatti0wner2 жыл бұрын

    • 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.

      @prathikkannan3324@prathikkannan33242 жыл бұрын

  • this was uploaded on my b-day :D

    @SB-qh6cr@SB-qh6cr2 жыл бұрын

  • Finally understanding what is the meaning of converge and diverge lol

    @chrislee7325@chrislee73253 жыл бұрын

  • I found this helpful, also...I love you.

    @Gizzlebear2U@Gizzlebear2U5 күн бұрын

  • Thanks!

    @kevinsolie2208@kevinsolie22082 жыл бұрын

  • 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.

    @ashwinkotha3388@ashwinkotha33885 ай бұрын

  • thank you very much!

    @gulyatanbayeva@gulyatanbayeva3 жыл бұрын

  • Thank you

    @GentilleKubwayezu@GentilleKubwayezu8 ай бұрын

  • thank you legend

    @SeekTranscendence@SeekTranscendence2 жыл бұрын

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

    @ethioabyssinia9630@ethioabyssinia96302 жыл бұрын

  • I am emailing this to my prof.

    @arekhandiaevidence5664@arekhandiaevidence56643 жыл бұрын

  • I don't understand the limits can you please explain and how to plot it in calcu?

    @vianahrica5491@vianahrica54916 ай бұрын

  • lifesaver fr fr😭😭

    @kandievicky7465@kandievicky74652 жыл бұрын

  • Thank you king

    @elizabethgevorgyan5165@elizabethgevorgyan51653 жыл бұрын

  • GOD BLESS YOU MAN

    @alvarobusquets@alvarobusquets Жыл бұрын

  • Please, make more videos on Series

    @nihatdonmezov8354@nihatdonmezov83542 жыл бұрын

  • 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.

    @RealSugam@RealSugam3 жыл бұрын

  • i love u guys fr life saver : )

    @Melanie-sk7qh@Melanie-sk7qh3 жыл бұрын

    • Hi

      @ethioupdatedinfo.@ethioupdatedinfo.3 жыл бұрын

  • You are legend

    @mousa6411@mousa6411 Жыл бұрын

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

    @teamstudent4555@teamstudent45552 жыл бұрын

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

    @kristoffcolinayo9713@kristoffcolinayo9713 Жыл бұрын

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

    @desireeannnieto7971@desireeannnieto797111 ай бұрын

  • 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?

    @nyambayartogtohtur1525@nyambayartogtohtur1525Ай бұрын

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

    @noahmaxario1448@noahmaxario144815 күн бұрын

  • I love this topic

    @kortezmayfield@kortezmayfield3 жыл бұрын

  • 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.

    @Elicruz2@Elicruz22 жыл бұрын

    • 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.

      @xinpingdonohoe3978@xinpingdonohoe39782 жыл бұрын

  • 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. ❤

    @blindpanda9084@blindpanda908411 ай бұрын

  • The Goat

    @user-tj2nk1he6z@user-tj2nk1he6zАй бұрын

  • you help me so much through math

    @med9922@med99222 жыл бұрын

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

    @rodneshajackon6598@rodneshajackon65983 жыл бұрын

  • Thanks, this really helped me.

    @srisources223@srisources2233 жыл бұрын

    • Bro you havent even watched this😑🤣🤣

      @hamzazahidi5404@hamzazahidi54043 жыл бұрын

    • @@hamzazahidi5404 Yeah, Series-ly

      @krupt5995@krupt59953 жыл бұрын

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

      @srisources223@srisources2233 жыл бұрын

    • @@hamzazahidi5404 I worded it differently

      @srisources223@srisources2233 жыл бұрын

    • @@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.

      @krupt5995@krupt59953 жыл бұрын

  • 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....

    @kabirsethi2608@kabirsethi26082 жыл бұрын

    • 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.

      @xinpingdonohoe3978@xinpingdonohoe39782 жыл бұрын

  • Dela Cruz, Adrian C. BSECE - 2B

    @adriandelacruz3041@adriandelacruz304111 ай бұрын

  • Dela Cruz, Froilan Arnel M. BSECE-2C

    @froilanarneldelacruz@froilanarneldelacruz11 ай бұрын

  • thanks

    @vivekkumar-si7tn@vivekkumar-si7tn Жыл бұрын

  • 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 🤧

    @fatima242@fatima2427 ай бұрын

  • Pedragosa, Rinoa F. BSECE-2E

    @ree5127@ree512711 ай бұрын

  • CASIA, AXLE JADE D. BS-ECE 2B

    @aksol7267@aksol726711 ай бұрын

  • Velasquez, Miguel Angelo A. BSECE-2D

    @miguelangelovelasquez4708@miguelangelovelasquez470811 ай бұрын

  • Gunita, Gillian C. BSECE - 2D

    @gilliangunita7627@gilliangunita762711 ай бұрын

  • Dela Cruz, Alexandre Jr. BSECE - 2C

    @alexandredelacruzTUP@alexandredelacruzTUP11 ай бұрын

  • Villarin, Paul Patrick W. BSECE 2B

    @Garfunnckel@Garfunnckel11 ай бұрын

  • Teves, Juan Miguel B. BSECE-2E

    @jmteves3778@jmteves377811 ай бұрын
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