Harmonic Series

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/jofOlZuLa9N9mNE Final Exams and Video Playlists: www.video-tutor.net/

[@girth8613]

Coming back to this video 1 year after passing Calc 2. I am studying the Harmonic Series as a part of my Algorithms course - This is so amazing now. Everything makes sense now.

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an outstanding video/lecture on the Harmonic Series in Calculus Two. This is a well-known series in all of Calculus. In the final analysis of the Harmonic Series at the 2:25 minute mark, there is an absolute value sign missing after the Ln. Professor Organic Chemistry Tutor, please correct this small error in the video.

[@zappist751]

this video is 5 years old bro

[@Sometimes2242]

Would it be necessary since in this example the value of n is always positive since the series starts at 1 and continues to move in a positive direction?

[@tgnuelakes]

That's how my teacher taught me: 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8… 1 + 1/2 +(1/3 + 1/4)+(1/5 + 1/6 + 1/7 + 1/8)… each bracket include twice more terms than the previous, each brackets are slightly larger than 1/2. Approximately it become 1+ 1/2 + 1/2 + 1/2…

[@cat1800]

And since the second serie is divergent then the harmonic serie is also divergent, clever proof !

[@pipertripp]

What's really cool to me is that this proof dates back to 1350. A french dude named Nicole Oresme came up with this approach long before logs or calculus were invented. The integral test approach is also cool, but I really like Oresme's proof for its elegance and use of simple ideas rather than the complicated machinery of integral calculus.

[@aishasaddiqa8345]

I just cannot tell you how much you've helped me in understanding all my semester course of calculus 2, i took concepts and practiced my exercise from my book, Jazak Allahu khairan kasira You're really a great teacher, No teacher in urdu language had explained these concepts upto this accuracy, I'm obsessed, i used to love all my maths Teachers bcz it's my favourite subject and so you my teacher, Stay Blessed 🌼

[@zackcarl7861]

Urdu teachers can't teach bcs they fraud 😆 ,the whole language is just a world play

[@aishasaddiqa8345]

@@zackcarl7861 have u done??🤦

[@inajefflymanner]

C-C-G-C-E-G-C-E-G-Bb-C... the other harmonic series

[@larskronke]

It's actually the same series, you're dividing the frequency of the tone by 2 for the octave, 3 for the 5th, by 4 for another octave, 5, 6, 7 and so on...

[@UltimateLuigi9426]

@@larskronke 🤓

[@philipschlaepfer9866]

@@UltimateLuigi9426this is literally a fucking math video

[@philipschlaepfer9866]

@@UltimateLuigi9426this is literally a fucking math video

[@drakenailling4276]

precisely

[@honn5761]

Me in 10th grade: *clicks on video to learn Harmon series math* Also me 1 minute in: *reads comments because its confusing* wait, this is calculus ?!

[@orangethew]

hi finsihed 12th grade?

[@mbenitez6722]

could you also have used the p-series? if ' 0 < p

[@물고기-p4f]

p-series is derived from integration test

[@arjay_2002]

@@물고기-p4f so yes?

[@물고기-p4f]

@@arjay_2002 no, because it would be a circular reasoning

[@arjay_2002]

@@물고기-p4f what to do then?

[@물고기-p4f]

@@arjay_2002 You can only do what's on the video

[@curtpiazza1688]

Excellent quick lesson..thanx!! 😊

[@TheFarmanimalfriend]

The harmonic series (1/n) as n => infinity, while it appears to converge to zero, actually diverges by never converging on one number. It has been widely accepted for the last 750 years, as written by Nicole Oresme, as n -> infinity, the sum of terms that equal 1/2 becomes infinitely large ( 2 x [1/4], 4 x [1/8], 8 x [1/16] . . . => .5+.5+.5 . . .) and, thus, diverges. Going over the calculus I used for my degree in Biochemistry, I came upon inconsistencies that were puzzling. So I created a series that exactly matches the one created by Nicole Oresme. My series starts at n=2, . It can be reduced to is a p series where p is always > 1 so this series converges to zero. As this new series is always less than the harmonic series and it converges (to zero), it says nothing about the harmonic series diverging. I think Nicole Oresme made an error and could not correct it because he was in residence with Charles 5, the king of France and had already told the king about his proof. He probably would have been tortured and/or executed for misleading the king if he admitted his error. To his disbelief (and relief) nobody ever caught his mistake. Use of a computer makes this more apparent, but is not necessary. The series that is less than the harmonic series converges and says nothing the harmonic series diverging. It is obvious, to me, that there is no need for all this extra work. As n gets infinitely large in the harmonic series, 1/n gets infinitely small and its addition to the existing number will change its value so that the harmonic series never attains a specific number, which is why it diverges.

[@ian.ambrose]

Thank you. Nicole Oresme's proof makes no sense for me either.

[@dabs4270]

1/2^n also gets infinitely small, so by your logic 1/2 + 1/4 + 1/8... also diverges, which clearly is not true. in fact your logic would tell us that every single infinite series would always diverge

[@josuequintero-td5gh]

Wow, you're not even a math major and you think you can challenge a well established proof, one which you're totally wrong about btw. The proof goes like this: Consider the partial sum s_(2^n): s_2 = 1 + 1/2 s_4 = 1 + 1/2 + (1/3 + 1/4) > 1 + 1/2 + (1/4 + 1/4) = 1 + 2/2 s_8 = 1 + 1/3 + (1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8) > 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8) = 1 + 3/2 And we can see that in general, s_2^n > 1 + n/2. This shows that s_2^n -> inf as n -> inf, so {s_n} is divergent.

[@harrabi15]

your last line is incorrect my friend. You can't just assume that because the numbers get smaller and smaller then their sum diverges. sum of 1/n^2 is an easy way to disprove your claim. The numbers get smaller and smaller yet their sum is not divergent. It's pi^2/6.

[@TheFarmanimalfriend]

@@harrabi15 you’re crazy, take your medication.

[@xilver3]

Could you increase the volume of your audio on your future videos, pls

[@kevinnguyen552]

Amazing! InStResTiNg! Lamentable! Onga bonga!!!

[@segmentsAndCurves]

Oh god no! NOOOOO!

[@bachagain1685]

I was expecting to find our species here.

[@notalinglingwannabe5028]

Ling ling

[@mr.prince8701]

great video. I used the P-series test also to show divergence.

[@anicetoaniceto1020]

You can't use p series to show it.

[@ElifM77]

@@anicetoaniceto1020 Yes you can, the power of n in this case is 1 and when the power is equal to 1 or smaller the series are divergent

[@TheFarmanimalfriend]

My use of the p series shows convergence which is indicative of how you have been mislead.

[@물고기-p4f]

@@ElifM77 Its circular reasoning. P series comes from integration test, which is actually proved from the assuption that harmonic series diverges.

[@anicetoaniceto1020]

You can't use the integral test to prove that the harmonic series diverges. You have to use partial sums to prove it. The integral test is circular reasoning. You can't use p series to show it because in order to use the p series you have to know what the sigma as n=1 to infinity of 1/n and 1/n^2 first to do that. So no integral test no p series. You can't just say the harmonic series diverges because you have to prove it.

[@MyAsdfqwe]

we can say and we did say. lol. this is not proof class.

[@DrtyTreeHuggr]

Typical theory... Math and science theory is all bs and can't be proven by random letters and signs... But u gotta belive it cus others say so. No proof needed. Sheep

[@luiswi]

Is there a formula for the harmonic series?

[@물고기-p4f]

@@twopie6911 is there an exact formula?

[@물고기-p4f]

@@twopie6911 that's said... always wished if there could be

[@longsleevethong1457]

Talking about AI

[@justwannahavefun3675]

POV: you are failing and still have no idea WHAT THE HELL IS GOING ON

[@malachimarasigan]

I was looking for C C G C E G. Oh by the way, the one im looking for is convergent :)

[@cameronmays5422]

I fucking hate math when I understand it, and I can't express why

[@longsleevethong1457]

Create a chart that graphs the harmonics of your struggle

[@anilkumarsharma8901]

In terms of LCM What is the solution??

[@anilkumarsharma8901]

In the terms of factorial What is solutions???

[@Shrimphat]

Isn’t it converged in p test??

[@DonchaLoveMilk]

No. It converges if P > 1 and diverges if P = or < 1.

[@Drew_Dolla]

@@DonchaLoveMilk facts

[@edwardsebastian8918]

Is Jacob's ladder, an aspect of the harmonic series? Intuition tells me it is quantum in nature.

[@venkateshbabu1504]

How to make it convergent using a different series mergers. Usually people are interested in damping.

[@elsabautista9347]

Well,do you have a harmonic series w/some examples

[@A_Sharaawy]

Thanks

[@iknowwhatyourethinking6404]

What this is different in my grade10 book it only says sum of harmonic sequenxe

[@Viper1924]

Your book deals with harmonic Sequences, this video is about Harmonic Series which is different than a sequence.

[@elsabautista9347]

And some formulas.

[@FreeDomSy-nk9ue]

You taught us that if: 1. the limit = 0 and 2. each term is smaller than the one before it, then it converges!!! It makes absolutely no sense that the harmonic series diverges...

[@longsleevethong1457]

Seems like harmony between two things going away from each other would more and more difficult to achieve

[@doji-san]

I don't buy it.. this series converges to a number and is not divergent

[@TheFarmanimalfriend]

The harmonic series is divergent. This is a bull shit explanation, because this new series converges to zero and is less than the harmonic series.

[@ggripen]

You stupid ass, it's divergent.

[@priyalsharma5817]

First liker , first commenter , first viewer

[@longsleevethong1457]

RIP

[@Vincent-np5dv]

formula of harmonic sum

[@barissw]

adam her şeyi biliyor ama her şeyi

[@strider3438]

Uncanny

[@neesamr6576]

good

[@TheFarmanimalfriend]

This is a bull shit explanation, because this new series converges to zero and is less than the harmonic series.

[@rosharchives5572]

whathafug