Binomial Series

[@TheOrganicChemistryTutor]

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[@chancegreyson8858]

I've been struggling with binomial series and how to write the general summation terms. But thank to you, I'm more confident with this now. I appreciate your videos so much. Keep up the good work !!!

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an outstanding introduction into the classical Binomial Series in Calculus Two. Rational and Square Root Functions can be represented as Power Seies with the aid of the Binomial Series. Practice problems and examples increases my understanding of this material. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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[@TonatapopyeniPopyeni]

My tutor in all my modules am grateful

[@mikeschieffer2644]

Around the 14:05 point you state that 5x4x3 is some sort of factorial. But to make it a factorial you need to have 5x4x3x2. Since you want to make the numerator have a 5! you would need to multiply the denominator by 2 also. This is why you need to have 2^(n+4) in the denominator instead of 2^(n+3).

[@90800905675]

Exactly, I was looking for this comment. The shift from 2^{n+3} to 2^{n+4} follows logically from the fact that the numerator is not 5! but actually 5!/2! which is identical to 5!/2, and thus explains the extra power of 2 in the denominator. Great video though!

[@marcorudyanto1719]

yeah in the end he added the 1/2 after evaluating each term, making it 2^(n+4)

[@gartyqam]

@@marcorudyanto1719 thanks mannn

[@beachwave5705]

stop disrespecting our god like that he explained that the factorial was incorrect thus thats why he literally showed us how to fix the problem

[@memduhylmaz8951]

From 14:00 to 22:44, instead of just saying that "we are multiplying both top and bottom side of the fraction by 2 to generate a factorial on the top" you made it as confusing as if that was a part of the way people should take for this kind of problems. I appreciate your tutorials, they are so helpful and simple mostly. I think you were tired or not focused enough for this time (which I don't have any problem with it, things happens) but if you could at least pin a comment about this confusion it could be helpful. I wanna thank you for your work, even 6 year from now it still helps. ❤

[@duyquangbui5297]

Thank you so much. Your video is so great. The second example made me a little crazy, but I understood clearly what do you explain? Your explanation is very detailed and easy to understand.

[@pooransingh1882]

An excellent exposition of the principles of the binomial series with many examples for reinforcement.

[@rajendramisir3530]

Excellent explanation and method of solving these problems. Efficient problem solving. Thank you, JG.

[@beachwave5705]

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[@beachwave5705]

@@WarriorBane Thanks man, i ended up getting the second highest score in the class, it was a grind for sure. got A's in rest of my classes gg

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[@zarifchowdhury1468]

14:35 it won't be (n+2)! as the multiplication ends at 3, there is no '2x1'. So it will be '(n+2)!/2' , although this is later fixed by dividing with 2. This was the mistake that required you to later divide by 2.

[@AmirJacob_94]

Thanks! I was wondering if there was a way to stop the factorial from going all the way to 1!

[@Brandoniafudgel]

I was wondering why he didn't multiply the LHS as well to maintain equality when he did that step. Thanks for clarifying the mistake he made.

[@honestman1224]

I like how he pretends to forget so that we realize it is important.

[@jessicasouthard6201]

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[@BlastinRope]

this shit is like fucking arcane black magic when the college lecturer does it but its simple arithmetic and algebra when you do it

[@makisekurisu8594]

Can you do integrating and differentiating binomial series?

[@_hoxin_]

Great tutorial! I have a question though, if the "x" variable in a binomial series were to be raised to a power, say x^3 etc... would that change the method for writing out the sequence? A more specific example would being to use a binomial series to find the MacLaurin series of : (1+x^3)^(1/2).

[@alealejre]

that would just be the new x the same as x/2

[@TheQueenIsWithin]

I think you'd have to write it as cube root of 1+ x^3

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thank you very much. very clear and well illustrated video.

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22:40 ... I feel you dude xD. Legendary tutor.

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the scientist you do

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Great explanation 🔥

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Boss pls how do you know the number of terms to stop thank you for this content Elaborate and Explicit

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Thanks!

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[@abdohazem3655]

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[@kameronbriggs235]

One of the problems was straight up bending my mind. I couldnt deal with thay first term being different.

[@christiancarter255]

How does -1 come before that? 41:55

[@louis4798]

I have the same question.

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[@technoviper4939]

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Who was your tutor??!

[@ServitorSkull]

Why just 5 terms though at 2:34?

[@mwansachikonde4193]

Great video, what do i do when I'm told to Expand a similar binomial and also state the set of values of 𝑥 for which each expansion is valid. Anyone else can help me with this...

[@Do-Some-Change]

When are you gonna reveal your face. Love you

[@frugelberg3816]

At 42:00 where'd you get the negative 1 from?

[@tiago001pessoa]

did you figure that out? i'm wondering about that as well...

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Do you tutor?

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[@noahd8673]

I dont under stand ur sum notation for sqrt(1-x), like based on it it would seem that 3*5 *....(2n-3) would be part of every term staring from n=2, but 3*5 isnt not part of the term n=2, it doesn't make any sense

[@scarlet6791]

I have the same question

[@tiago001pessoa]

at 27:40 why is n=1 (-1)? it's clearly a positive number...

[@zovuyofani2822]

For the first sum in the beginning of the video ,why did we add 3x^2 and 5x^4 instead of subtracting them??

[@Aaron-v8m9j]

because two negatives make a positive and its not "we" its him hes the teacher and know more than "us"

[@Bbbbbbbbbbhhhhhhh]

@@Aaron-v8m9jwhat? But is there anything else even timsing the 3? The -2 cancelled because of the other 2 on the bottom meaning the top -3 would of been on its own right?

[@saberspeed77]

skip one math lecture and u end up not knowing what's going on lol

[@bakdauletabdikhan]

could I write that [1*2*5*... * (3n-4)] like this (3(n)!-4) ? Interesting !?

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Is this math 321?

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Nice work ma nigga. I appreciate do much hommie!

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lmfao

[@rafaelotani7444]

in the last example you have (1-x)^(1/2). But the pattern is (1 + X)^m so, the fact that ou have a minus instead of a plus doesen't change things?

[@daminisharma6096]

No, it doesn't change anything .....u can simply take that negative sign in bracket ....by doing this u have a positive sign outside

[@felixfelix3421]

at 3:04 did he mess up on the 3x^2 should it not be negative?

[@Aaron-v8m9j]

no because it belongs in the formula. He's just simplifying the fraction. Its positive because 2 negatives multiplied by each other give you a positive.

[@mel-kr2xu]

42:00 where did he get the -1 from ?

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i cry

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God is his creator and idolatry is not the move 😬

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[@goodc.2853]

At 36:47, I'm a little confused as to how the arithmetic series helps you determine where the series starts?

[@bikashadhikari1822]

The pattern of odd numbers starts at n=1 but not n=0. you can even start the series at n=2 if you're willing to.

[@chaiyewhuan7622]

20:20

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[@TonatapopyeniPopyeni]

My tutor in all my modules am grateful