Convergence and Divergence: The Return of Sequences and Series

[@mainulislam6765]

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 .

[@saeedahmed-9290]

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

[@calculus8399]

​@@jonathanlimjun6238 what do you know about convergence

[@emmaell123]

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

[@Kiky_MedPhysicist]

Thank you sir for your dedication and for making this free! 🙏

[@jamvibes3550]

Hi prof dave, your channel helped me a lot in my study. I humbly for a request a video explaining the fourier series. I will wait for it. Thank you so much.

[@32_gurjotsingh82]

refer to 3b1b video on fouries series...

[@mathew_pang]

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

[@IslamicLifestylevibess]

same here

[@Vinickw]

This is the limit of the sequence, not the series. It means that for a very big _n,_ the sequence will be approximately {...1/5, 1/5, 1/5...}, and adding infinitely many 1/5 will result in infinity.

[@ClumpypooCP]

"let's converge a little"

[@juraijbinjamal5313]

Good one

[@f3ralp1g3on6]

converge me daddy UwU

[@The-Cookie]

@@f3ralp1g3on6 ayo- 🤨🤚

[@nelayapu5789]

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

[@hailabseyoum5746]

great lecture! Thank you professor a lot!

[@angadthandi2281]

@@jonathanlimjun6238 Nice bot

[@nnofficial2414]

It was a good revision! Great job 👏

[@johnholme783]

Crystal clear! Thank you!

[@vianekabanda8348]

This professor is good. I like this video

[@harismasoom6634]

PROFESSOR you explained it so beautifully. Thanks.

[@Ashish-hl7rk]

so if the resulting series is zero it is convergent?

[@TanJunYu]

thank you so much!

[@ECEAbhishekKumar]

Thank you 😊👍 so much from India.

[@TheBrammiej]

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

[@ProfessorDaveExplains]

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

[@TheBrammiej]

Professor Dave Explains Hugs!

[@MathCuriousity]

Would someone mind explaining why it is that every power series is a Taylor series? (I know every Taylor series is a power series but I’m wondering why the reverse is true - and without invoking heavy analysis stuff)!

[@nweniaung9621]

Thank.You Professor

[@niaala]

Thank you so much.really helpful

[@pluto4301]

0:50 bold of you to assume that 😅

[@thisisnyx]

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

[@geektoys370]

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

[@sachinrajpandey5242]

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.

[@user-cr8bd9qk1r]

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

[@ericard4165]

Like your animations

[@ccbgaming6994]

First equation = -1/12 ;)

[@debajyotisarkar1145]

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.

[@ProfessorDaveExplains]

I did that too, check the mathematics playlist!

[@jamebello9869]

so helpful

[@AlessandroZir]

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

[@rinr3300]

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

[@Attalla-t9b]

In the beginning, he was talking about sequence. At the end, he was talking about series (It seems like they have different criteria for divergence/convergence)

[@salaa23]

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

[@umararshad9567]

convergent = limit does not exist

[@fishlasagna7368]

Thank you 🙏🙏🙏

[@davideveringham3827]

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

[@beetaff7841]

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

[@samitkumar1170]

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

[@AnAzsproduction]

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

[@riyabiswas906]

Thankyou sir for such a simplified explanation.

[@courageandpeace1944]

love from India

[@jontedeakin1986]

whats the name of the theorem at 7:17?

[@Sarah-re7cg]

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]

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

[@jah_141]

this stuff is confusing idk if i can do it man but i have to for school

[@jawwadshahed]

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

[@sandeepanpoddercse3819]

thanks sir

[@duelingo8731]

you reduce my stress levels by 10000%

[@supreethmv]

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.

[@shankarabhat7505]

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

[@ProfessorDaveExplains]

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

[@adventuresofgaara8936]

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

[@iyasuwalalign2860]

how could i explain my love to this wonderful man

[@Bhanuday-pp1dj]

Love from india

[@samjames1253]

Thank you so much!!!

[@GodbornNoven]

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

[@ckarcher4504]

7:05 how to get that answer?

[@nabanitagoswami6652]

You are very helpful 😄😄❤️....

[@chaosend3815]

Great video! your explanation is very easy to understand

[@TheBluePhoenix008]

you gotta do more of these man

[@leejunzhao]

2:54 the sequences should start from 1

[@antonioochoa2673]

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

[@sidharthmohanty6434]

Thanks loved it.

[@thestar001Official]

I lost it at "In fact,..." 7:10 😪

[@noahgsolomon]

He knows a lot about all kinds of stuff

[@curtpiazza1688]

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

[@badreddineadrham9605]

1+2+3+4+5+……= -1/12 😢

[@Has_Chemist2.0]

How can math be amazing like this 😍

[@annaV513]

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

[@fernanmontevista204]

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

[@ProfessorDaveExplains]

Yep!

[@mahinduliyanage1583]

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

[@adriaaan.n]

Jujutsu kaisen brought me here

[@dareto2181]

수학이랑 영어를 합하니 배로 좆같네;;

[@julytdalida4860]

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

[@Diviner-ip2pq]

❤❤❤❤❤❤❤❤❤❤❤

[@imbreakingdown2683]

2:17 Why Am I laughing so hard

[@JoanKemon]

THANK YOU SO MUCH

[@koamivikeledome]

🙏

[@reengaesh7545]

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

[@niekbeijloos8355]

Very clear explanation, thanks!

[@cavendis3423]

nice

[@мир-н3л4х]

which playlist is this video in?????

[@ProfessorDaveExplains]

math

[@nononnomonohjghdgdshrsrhsjgd]

i like everything in the way how you explain!

[@douglasposho9299]

Thanks for the knowledge you have shared with me.

[@katunduchabala7266]

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

[@MimiMimi-ss7jk]

Thaaaaanks a lot🙏Finally,I understood!

[@zeinebkefeya1946]

Perfectly explainedd🔥

[@إيمانإيمان-ف4ي]

Excellent explanation

[@ishiitapal]

thank you

[@shahrukhkhanshahrukh3504]

great man

[@MissOk777]

Great explanation !

[@sedeqalsakkf9315]

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

[@RickyRicheRebelle]

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

[@irfankadem3628]

GREAT WORK KEEP UP!

[@danielgilder8672]

This helped me with my Alevel

[@JillianRiccio-rv3nu]

🙏🏻 🙏🏻 🙏🏻

[@joongi9839]

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

[@ProfessorDaveExplains]

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.

[@harrisonbennett7122]

Thank you

[@Mr_Passionate]

[@PratimMukherjee]

Simple af

[@murphy6177]

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😅

[@gautamchettiar4150]

wasn't it -1/12

[@wolframalpha8634]

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!

[@gautamchettiar4150]

@@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

[@wolframalpha8634]

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

[@gautamchettiar4150]

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

[@wolframalpha8634]

@@gautamchettiar4150 thanks! I'll watch it

[@ericard4165]

Hey professor Dave, what else after calculus in this course

[@ProfessorDaveExplains]

linear algebra! and then hopefully differential equations.

[@ericard4165]

thanks they're really helpful

[@Oscar-gx2yf]

Thank you Lord Farquad you are the best!