@@TheDslide, yes, you were rapid, a second could be long enough. reality exists, well can be said to exist, thanks to your recognising truth about it, and thanks to your recognising the lies too. as to what everyone thinks about it, some of us had as a first thought drawing a / through the = . great clickbait for math lovers.
I LOVE how you take a break from calculus to appreciate the humble Algebra! You have truly opened my mind to appreciate algebra once again!!! Cannot thank you once again since I am a regular viewer. YOU NEVER DISAPPOINT!!!!!
I really like how you explain theorethical math to a huge variety of people and I think everyone can understand it and not only those who did it in school alread. I think it´s really nice to learn new things even if you don´t need it in most cases because we train our brains with this and your love for math makes it even better to understand and makes me happy aswell. Great job keep up the work!
For those who are intrested to see a rigorous proof of the theorem, with detailed explanation of every step check a video on my channel called: Calculus 1: The Binomial Expansion Formula Derivation and Proof it is a part of the calculus playlist that I'm recording
Haha! you got me....I was so stunned I actually PAUSED the video 2 seconds after you wrote (a+b)^2 = a^2+b^2.... wondering what the heck had happened. Also scrolled down expecting to see a plethora of haters in the comments! So, I was quite surprised at the comments, and realized that I needed to watch more of the video before being surprised :) I really dig your humor! And it's not even April Fools Day....
also the the sequence 1 2 1 is the number of vertices you span when travelling diagonally from a vertex to the opposite vertex in a square. as a matter of fact each row in pascal's triangle represents an n-dimensional cube, so 1+5+10+10+5+1 = 32 or 2^5 or the number of vertices of the 5-dimensional cube.
thank you for this. I am trying to stop just mugging formulas my teacher is feeding me and trying to understand how formula is found. You are one of the only videos explaining derivation in so much detail. 🙏
I was a bit stressed out until he crossed out a²+b² Edit: @ 12:43, when you've written n! = n*(n-1)*...*3*2*1, strictly speaking it will only be correct for n >= 5 right?
I got so confused why you were covering this since I learned it when I was in grade 11, but then I remembered my highschool education was very weird compared to most places and isn't even taught that way here anymore.
For those who are intrested to see a rigorous proof of the theorem, with detailed explanation of every step check a video on my channel called: Calculus 1: The Binomial Expansion Formula Derivation and Proof it is a part of the calculus playlist that I'm recording
@@anusheelsolanki1 no, it does for all rows. Consider 1 4 6 4 1.when we call it a power of 11, what we really mean is (1×10^4 + 4×10^3 + 6×10^2 + 4×10^1 + 1×10^0) is a power of 11. Now consider row 5. The number here is 1 5 10 10 5 1. If you do the same (convert it into decimal), it becomes (1×10^5 + 5×10^4 + 10×10^3+ 10*10^2 +5×10^1 + 1×10^0) which is 161051, which is a power of 11.
Only if you take by decimal expansion, row 5, 1 5 10 10 5 1 1*100000+5*10000+10*1000+10*100+5*10+1*1=11^5 Explanaiton: so because each row can be expressed as binominal expansion, let a=10 and b=1 Then (a+b)^n=(10+1)^n=11^n
A lot of patterns appear in pascals triangle like the sun are powers of 2, the fibonnaci sequence appears in the sum of special diagonals, serpeinski's triangle with odd/even, some patterns that are close to serpeinski's triangle appear with multiples of other numbers, 3, 4, 5,... The (real) diagonales show the triangular(2D), tetrahedron (3D triangle), pentatope (4D triangle),... And pascals triangle can be written as combinatorics,... A lot of same patterns appear in higher dimensions of pascals triangle, pascal simplexes
Dear blackpenredpen, Look at 6:49. I found it interesting when I was looking at the rows only. The first row contains 1=(11^0), (here n=0), 2nd row contains 2 digits 1 and 1 to make it 11=(11^1),(here n =1), 3rd row contains 3 digits 1,2 and 1 to make it 121=(11^2),(here n=2), 4th row has 1,3,3,1 to make 1331=(11^3),(n=3), 5th row is 14641=(11^4),(n=4) and so on . Is it a coincidence to get 11's powers raised to n value every time?
I does get a little more awkward when you have two digit numbers in the triangle, but if you carry to the right it still works. You want to know why? Here is a tip on how to get started on the answer: 11^n = (10 + 1)^n If you need another tip: expand the above using the Binomial Theorem :) You might also notice that each row sums up to 2^n, wonder why?
Each row sums up to 2^n. That easy to understand because expansion of (1+x)^n gives that result when x=1. That gives as sum of co officiants as 2^n. Okky now I understand both of your statements. Thank you.
You need a completely different approach for fractional and negative powers. It's an infinite series where the answer is the sum. If you have (a+bx)^k, you need to convert it to the following (a^k)(1+(b/a)x)^k and then the nth term is (a^k)+(a^k)[ ((k)(k-1)(k-2).....(k-n)(x^n)) / n! ]
Sir,can u give an explanation about why volume formula can use disk method ,but surface area we cannot use cylinder to approximate instead of frustum since it is infinite cylinder
The answer goes to infinity, so it diverges. You can try checking it on your graphing calculator as fnInt(tan(x),x,0,pi/2), but the answer will show up as error, tolerance not met, or whatever answer it says there.
@@blackpenredpen And I think (a+b)^2 = a^2 + b^2 if ab =0 mod n (so for example mod ab, or if a=xy then xb or yb does it. edit: one of our abstract algebra homework questions was about proving a similar result to this but I forget the details)
Answer this please. A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.
Hiii im kinda new to this channel you seem really awesome and I kinda understand your lessons. I was just wondering if you have videos or are you planning to make videos tutoring basic calculus. And if you do, do you have a playlist for it. I'm still a freshman trying to go for engineering course thank youuu
Hey, I was wondering if you could do a video on the cubic formula, or just a way in general to solve cubic equations. I've been confused about this and haven't been able to find any videos that are easy to understand. Thanks!
Hello blackpenredpen. Why zero can't be used when applying binomial expansion to evaluate (1.01)4. I know this is easy when we express (1.01)⁴ as (1+ 0.01)⁴. Suppose we wish to express (1.01)⁴ as (0 + 1.01)⁴. Why this gives zero as a answer.
Please:: A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.
So, when you have a certain number of x's and a certain number of y's (partitions of n of course) you have multiple ways of representing that only because there are multiple x's and y's not because the position of those x's and y's matters obviously. Combinations are literally just pairings of n elements into unique sets of size k hence n choose k. Although, in the case of the binomial theorem the size of the set is always n you simply choose k out of n elements to be different; x not y or the other way around.
Yep, that's correct. Some people confuse this with permutations. Both permutations and combinations are different due to the ordering. If you're trying to find this on your calculator, the formula that he wrote in this video is denoted as nCr, which is n!/(r!(n-r)!). Permutation is denoted as nPr, which is n!/(n-r)!. n and r must positive integers. 0!=1 by definitely of the empty set.
I need help. A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.
I am just interested: Is there any way to use the binomial theorem for n being just racional? Maybe with calculating factorial with gamma funktion? Well there are some more problems but I guess there are smarter people than me which could help me x)
i know (a+b)^2 = a^2 + b^2 is a false statement, but what are the values of a and b such that this equation is true? How would that answer compare if a and b could be the same number to if a and b have to be different numbers?
If (a+b)^2 = a^2+b^2 So a^2+2ab+b^2 = a^2+b^2 That means that 2ab = 0 And so a = 0 or b = 0 In that case it would be equal but same as only a (or b) so not so useful...
(a+b)² = a²+b²
That's enough TH-cam for today.
Comment of the day!
😂😂😂😂😂
lol
lol mate
(1+0)^2 = 1 = 1^2 + 0^2
It's true.
(a+b)² = a²+b²
I was questioning reality for a second XD
Same
That's actually good science. Always question what everyone thinks reality is:)
@@neilgerace355 agreed but it can drive u mad if u do it too much
Accepts when a or b = 0
@@TheDslide, yes, you were rapid, a second could be long enough.
reality exists, well can be said to exist, thanks to your recognising truth about it, and thanks to your recognising the lies too.
as to what everyone thinks about it, some of us had as a first thought drawing a / through the = .
great clickbait for math lovers.
0:02 Newton was literally trembling and shaking
He literally shidded and farded himself
I almost had a stroke at the beginning D:
Breaking news: BlackpenRedpen loses all of its subscribers after saying that (a+b)^2=a^2+b^2.
They didn't try it for themselves first, so they haven't listened what bprp always says :)
Fluffy Massacre hahahahaha
2ab: "Am I a joke to you?"
I LOVE how you take a break from calculus to appreciate the humble Algebra! You have truly opened my mind to appreciate algebra once again!!! Cannot thank you once again since I am a regular viewer. YOU NEVER DISAPPOINT!!!!!
I love how you explain this in such a layman's term.
I really like how you explain theorethical math to a huge variety of people and I think everyone can understand it and not only those who did it in school alread. I think it´s really nice to learn new things even if you don´t need it in most cases because we train our brains with this and your love for math makes it even better to understand and makes me happy aswell.
Great job keep up the work!
For those who are intrested to see a rigorous proof of the theorem, with detailed explanation of every step check a video
on my channel called:
Calculus 1: The Binomial Expansion Formula Derivation and Proof
it is a part of the calculus playlist that I'm recording
This video is so educative. Pascal's triangle, factoriels, sign for summation, combinatirics and powers in one video...
Sanel Prtenjača yea, this had so much and I was so excited to record 3 parts all in one day!!
Haha! you got me....I was so stunned I actually PAUSED the video 2 seconds after you wrote (a+b)^2 = a^2+b^2.... wondering what the heck had happened. Also scrolled down expecting to see a plethora of haters in the comments! So, I was quite surprised at the comments, and realized that I needed to watch more of the video before being surprised :) I really dig your humor! And it's not even April Fools Day....
also the the sequence 1 2 1 is the number of vertices you span when travelling diagonally from a vertex to the opposite vertex in a square. as a matter of fact each row in pascal's triangle represents an n-dimensional cube, so 1+5+10+10+5+1 = 32 or 2^5 or the number of vertices of the 5-dimensional cube.
thank you for this. I am trying to stop just mugging formulas my teacher is feeding me and trying to understand how formula is found. You are one of the only videos explaining derivation in so much detail. 🙏
I thought it was April fools for a second
Very nice and healthy lecture, helped me to conquer my syllabus, which was looking very difficult in my study material. Thanks Sir.
Oh wow. This brings back long forgotten memories of high school. Thank you for yet another incredibly entertaining video
Thank you!!! I am glad to hear it!! : )
I was a bit stressed out until he crossed out a²+b²
Edit: @ 12:43, when you've written n! = n*(n-1)*...*3*2*1, strictly speaking it will only be correct for n >= 5 right?
n = 1,2,3....
No not nessicarily, n just has to be greater then one. He just wrote that for the example, it can also be written as n!=n*(n-1)*...*1
@@rastaarmando7058 u didn't understood the joke sir!
I learned more in the first minute than 5 yrs of high school
*FIVE years*
What country are you from
Pulled a switcheroo with that first bit. My complex roots were quaking right there.
0:12 look at him smiling at our confusion
(a+b)^2 DOES equal a^2 + b^2 though...
...in a commutative ring of characteristic 2
The only context that really matters.
Or if a or b=0?
Or when a or b=0
Here’s the deal... your video was helpful and fun. Subscribed!
0:22 oh I loved those Dr Peyam clips, I remember watching this :D
TS 5:00...very important and oft missed point. You sir are really doing the lord's work here. One of the bwst maths channel out there on youtube.
Very Good explanation!!!!
I got so confused why you were covering this since I learned it when I was in grade 11, but then I remembered my highschool education was very weird compared to most places and isn't even taught that way here anymore.
If n is not a positive whole number, it should still be possible to apply the theorem, we just have to
「ｄｏ ｍｏｒｅ ｗｏｒｋ」
(Limits flashbacks intensifies)
Hahaha, nice one!!! And that's part 2 btw.
For those who are intrested to see a rigorous proof of the theorem, with detailed explanation of every step check a video
on my channel called:
Calculus 1: The Binomial Expansion Formula Derivation and Proof
it is a part of the calculus playlist that I'm recording
ARE YOU 3BLUE1BROWN???
Fun fact : Pascal's triangle gives the powers of 11
Only till the 4th row
@@anusheelsolanki1 no, it does for all rows. Consider 1 4 6 4 1.when we call it a power of 11, what we really mean is (1×10^4 + 4×10^3 + 6×10^2 + 4×10^1 + 1×10^0) is a power of 11.
Now consider row 5. The number here is
1 5 10 10 5 1. If you do the same (convert it into decimal), it becomes
(1×10^5 + 5×10^4 + 10×10^3+ 10*10^2 +5×10^1 + 1×10^0) which is 161051, which is a power of 11.
@@anusheelsolanki1 nope
Only if you take by decimal expansion, row 5, 1 5 10 10 5 1
1*100000+5*10000+10*1000+10*100+5*10+1*1=11^5
Explanaiton: so because each row can be expressed as binominal expansion, let a=10 and b=1
Then (a+b)^n=(10+1)^n=11^n
A lot of patterns appear in pascals triangle like the sun are powers of 2, the fibonnaci sequence appears in the sum of special diagonals, serpeinski's triangle with odd/even, some patterns that are close to serpeinski's triangle appear with multiples of other numbers, 3, 4, 5,... The (real) diagonales show the triangular(2D), tetrahedron (3D triangle), pentatope (4D triangle),... And pascals triangle can be written as combinatorics,... A lot of same patterns appear in higher dimensions of pascals triangle, pascal simplexes
OH MY GOODNESS WAIT......
I'M SUFFERING OF TRYING TO UNDERSTAND THIS THEORY AND YOU'RE......
JUST MUCH THANKS 😭😭😭❤❤❤❤❤❤❤❤❤
I LOVE YOU REALLY 😹😭❤💛💜🌻
You are the best teacher
La mejor explicación que he escuchado
Dear blackpenredpen,
Look at 6:49. I found it interesting when I was looking at the rows only. The first row contains 1=(11^0), (here n=0),
2nd row contains 2 digits 1 and 1 to make it 11=(11^1),(here n =1),
3rd row contains 3 digits 1,2 and 1 to make it 121=(11^2),(here n=2),
4th row has 1,3,3,1 to make 1331=(11^3),(n=3),
5th row is 14641=(11^4),(n=4) and so on
. Is it a coincidence to get 11's powers raised to n value every time?
I does get a little more awkward when you have two digit numbers in the triangle, but if you carry to the right it still works.
You want to know why? Here is a tip on how to get started on the answer: 11^n = (10 + 1)^n
If you need another tip: expand the above using the Binomial Theorem :)
You might also notice that each row sums up to 2^n, wonder why?
Each row sums up to 2^n. That easy to understand because expansion of (1+x)^n gives that result when x=1. That gives as sum of co officiants as 2^n.
Okky now I understand both of your statements. Thank you.
That's really well explained! Thanks!
0:20 thank you so much I almost had a heart attack
I like this
Insert: good lighting
Finally a video I can understand and already know the solution of! Haha
MY HOMEWORK WAS ON THIS TODAY, YOU SAVED ME
You need a completely different approach for fractional and negative powers. It's an infinite series where the answer is the sum. If you have (a+bx)^k, you need to convert it to the following (a^k)(1+(b/a)x)^k and then the nth term is (a^k)+(a^k)[ ((k)(k-1)(k-2).....(k-n)(x^n)) / n! ]
You should do a^n + b^n or a^n - b^n next
Factor those?
@@blackpenredpen yeah.
(a+b)^2 = a^2 + b^2 was too uncomfortable to watch. I had to cover it until you erased it. Thank you for not torturing me too long.
Thank you
Cant wait for the general formula
Its in the description now. You can have n being -2
Very good Explanation BUD
Hello...sir you are great...
Love from india....
Thank you for good math video.
Sir,can u give an explanation about why volume formula can use disk method ,but surface area we cannot use cylinder to approximate instead of frustum since it is infinite cylinder
omg! this was very useful; thanks a lot; 🤸🙌🧘💕💕
Such an amazing video❤️❤️, please do more videos on combinatorics and discrete mathematics.
helpful review, thank you :)
I feel like I understand everything in your videos and then I look at my homework and cry
Bprp-(a+b)²=a²+b²
Me-Nani?
Omae wa mou shindeiru?
The illustration you show in the beginning is very helpful but it can be explained much easier by using mathematics of the vedic to illustrate
0:20 good save i almost had a stroke
Please what channel did you refer to in your last two posts? Was it Fresh Toadwalker?
Filip Kochan no
Derivation of cycloid's area through integration next please .love the videos ,even if i cant understand some of them,cheers.
Please calcul the integral from 0 to π/2 of tan(x) 🙏
Diverges
The answer goes to infinity, so it diverges. You can try checking it on your graphing calculator as fnInt(tan(x),x,0,pi/2), but the answer will show up as error, tolerance not met, or whatever answer it says there.
(a+b)^2 = a^2 + b^2 in certain cases (for example some modular arithmetic structures, or in vector analysis when a and b are perpendicular)
Matti Kauppinen mod 2
@@blackpenredpen And I think (a+b)^2 = a^2 + b^2 if ab =0 mod n (so for example mod ab, or if a=xy then xb or yb does it. edit: one of our abstract algebra homework questions was about proving a similar result to this but I forget the details)
Wow, I remember this. We can use this to derive the definition of the derivative using this formula for power rule.
Justin Lee
Yes. And we can also write e as a series.
0:00
I-I-Is that... the Overwatch theme ?
*_W O O O O O W ! ! ! ! !_*
I love Pascal’s Triangle... 😁
Answer this please.
A pyramid with a square base, 4 m on each side and four
equilateral triangular faces, sits on the level bottom of a lake at
a place where the lake is 10 m deep. Find the total force of the
water on each of the triangular faces.
this blew me away
Can you make a video on the Laplace transfer?
With the music and the way you said this is very easy, I almost believed you...
1willFALL : )))))
Learning this rn in gr12 data management
Hiii im kinda new to this channel you seem really awesome and I kinda understand your lessons. I was just wondering if you have videos or are you planning to make videos tutoring basic calculus. And if you do, do you have a playlist for it. I'm still a freshman trying to go for engineering course thank youuu
Jayvee Flores hi Jayvee and welcome !! Please see my description for my website and other resources. Thanks and hope you enjoy my content here
@@blackpenredpen Thank youu! Keep making videos your content is very awesome I am looking forward for more of your videos. Best wishes
When you said a^2+b^2=(a+b)^2, I was about to ring up the local exorcist to see if you were possessed, fortunately I kept watching
Does the XXYYY same to YYYXX ? count them all or just choose 1 of them, or I mean that the position is necessary for this case?
Please let this be a new series.
Nole Cuber
Yes. We will totally get a “series” out of this
Btw, part 2 is already in description
@@blackpenredpen pun intended;)?
15:30 We will get there eventually!
Hey, I was wondering if you could do a video on the cubic formula, or just a way in general to solve cubic equations. I've been confused about this and haven't been able to find any videos that are easy to understand.
Thanks!
Thank you for sooo a great video :)
I remember me learning that in high school!
Hello blackpenredpen.
Why zero can't be used when applying binomial expansion to evaluate (1.01)4.
I know this is easy when we express (1.01)⁴ as (1+ 0.01)⁴.
Suppose we wish to express (1.01)⁴ as (0 + 1.01)⁴. Why this gives zero as a answer.
Man you should do a video about polynomial theorem
Quitzé Chávez
Part 3 is about trinomial. And that pretty much it.
almost as good as 3
Definitely!
Tem algum vídeo demonstrando a fórmula do polinomio de leibniz .
Please::
A pyramid with a square base, 4 m on each side and four
equilateral triangular faces, sits on the level bottom of a lake at
a place where the lake is 10 m deep. Find the total force of the
water on each of the triangular faces.
So, when you have a certain number of x's and a certain number of y's (partitions of n of course) you have multiple ways of representing that only because there are multiple x's and y's not because the position of those x's and y's matters obviously. Combinations are literally just pairings of n elements into unique sets of size k hence n choose k. Although, in the case of the binomial theorem the size of the set is always n you simply choose k out of n elements to be different; x not y or the other way around.
Yep, that's correct. Some people confuse this with permutations. Both permutations and combinations are different due to the ordering. If you're trying to find this on your calculator, the formula that he wrote in this video is denoted as nCr, which is n!/(r!(n-r)!). Permutation is denoted as nPr, which is n!/(n-r)!. n and r must positive integers. 0!=1 by definitely of the empty set.
Can you explain Laplas transfer?
And thanks for you for all your videos.. Everyone watching you love learn and love you
Thank you again 🖤
Can you solve İMO problems? Have you got any achivement from that?
can u explain 8.25-8.37 , i dont really quite understand what do u mean 4 go down then got 2 something....
I need help.
A pyramid with a square base, 4 m on each side and four
equilateral triangular faces, sits on the level bottom of a lake at
a place where the lake is 10 m deep. Find the total force of the
water on each of the triangular faces.
At 19:30 it makes sense mathematically but my brain doesn't get it what he is saying. Can anyone explain it
15:33 So, you fourgot the four?
I did. Lol
Woooow amazing
I am just interested: Is there any way to use the binomial theorem for n being just racional? Maybe with calculating factorial with gamma funktion? Well there are some more problems but I guess there are smarter people than me which could help me x)
maybe youtube was listening during my math class today?
Lol must be
I studied this last year, 7th class
Thank for the heart sir, @blackpenredpen
Thanks for your great job! Could you please make video about Multinomial theorem (x1+x2+x3+x4+...+xm)^n. Thats would be wonderful, isn't it?
I'll try to tell the ans
Wait
3:51 well that six made me like 😳
I thought there will be a four
@blackpenbluepen do you take requests?
What about negative sign? Please explain.
Amazing!
17:02
Do you cover Generating Functions & the Multinomial Theorem anywhere?
Ivy Agnes Nguyen getting there
Ivy Agnes Nguyen do U have a specific problem?
We want more aboht this issue
As most of us know, this is very easy.
I seriously started questioning my entire mathematical knowledge in the first 30 seconds of the video...
i know (a+b)^2 = a^2 + b^2 is a false statement, but what are the values of a and b such that this equation is true? How would that answer compare if a and b could be the same number to if a and b have to be different numbers?
If (a+b)^2 = a^2+b^2
So a^2+2ab+b^2 = a^2+b^2
That means that 2ab = 0
And so a = 0 or b = 0
In that case it would be equal but same as only a (or b) so not so useful...