Я, русскоязычная казахстанка, ничего не понимающая в английском, сижу разбираю тему в интернете, чтобы объяснить её своему ребенку. Спасибо за Ваш труд.
Mathematical Induction is actually nice and cozy. Can be used in Calculus too! And I find it amazing (thou intimidating in inequalities because it confuses me.)
Proving the k case from k-1 is a tiny bit cleaner because you get a nice symmetry, but it obviously doesn't matter in the end. I did it with a lemma f(k) - f(k-1)=k^3.
you can use f(n)=an^4+bn^3+cn^2+dn+e then f(1)=1,f(2)=9,f(3)=36,f(4)=100,f(5)=225 then you can proof that a=1/4,b=1/2,c=1/4,d=0,e=0 =>f(n)=(n(n+1)/2)^2
I'm learning pre-calc before I go into calc next year and videos like yours are amazing! Your explanation and work is very easy to follow and so crip! Thank you so much and I'm subscribed!
Thats the thing which he explained lmao ... just you need to know that 1+2+3+4+5+...+n= n(n+1)/2 And there is a beautiful way to derive this above formula without any derivation or integration or higher mathematics!
Lol our teacher gives us only the left side and we have to figure what the right side is on our own, makes things a lot more interesting😂 You either have to already know the formula or test it and figure it out on the spot. Nice video!
Awesome video. It really put things into perspective. I have one problem though. I usually find a hard time to form the conjecture of the series. Like for instance, how did you get {n(n+1)}/2. I usually find a hard time figuring it out. Any help will be appreciated.
Take (a+bi)^4 this will give you and infinite list of values that will solve the equation where the real part is one leg, the imaginary part is the other leg, and the hypotenuse is the length.
5^4=(24)^2+7^2 is a counter example there are many counter examples u can generate them by using euclids formula consider (2mn, m^2-n^2, m^2+n^2) we want m^2+n^2=C^2 hence get another pythagorean triplet in form(m, n, C) plug it in to get A and B and you have it
Я, русскоязычная казахстанка, ничего не понимающая в английском, сижу разбираю тему в интернете, чтобы объяснить её своему ребенку. Спасибо за Ваш труд.
When I finally understood how we was checking the logic through Induction, I was getting HYPED as he was getting closer to solving for "n=k+1"
(k^2+4K+4) being factorised is also in the form (a^2+2ab+b^2) which upon reversing gives (k+2)^2 if you're not familiar with factorisation like me
Mathematical Induction is actually nice and cozy. Can be used in Calculus too! And I find it amazing (thou intimidating in inequalities because it confuses me.)
cozy, for me its a fire bit of hell
I proved the differentiation from first principles with induction. it was really challenging
Yeah it's true
It's not cozy for me
Yes
You just connected so many things in my brain. Thank you so so much
Your explanation is amazing. Succinct and detailed at the same time 🙏🏾
10^5 congratulations!!
Proving the k case from k-1 is a tiny bit cleaner because you get a nice symmetry, but it obviously doesn't matter in the end. I did it with a lemma f(k) - f(k-1)=k^3.
what does the box at the end means? is it just like Q.E.D.?
Yes.
wow! 曹老师让我第一次学会了这么强大的功能！
I love math induction! Super useful:D
Great teacher. i love maths
Baby Kwong thank you
I like your enthusiasm at the end.
You are such a good Teacher
you can use f(n)=an^4+bn^3+cn^2+dn+e
then f(1)=1,f(2)=9,f(3)=36,f(4)=100,f(5)=225
then you can proof that a=1/4,b=1/2,c=1/4,d=0,e=0
=>f(n)=(n(n+1)/2)^2
I just loved your spirit, energy and the way you are explaining things!! I wish you were my instructor instead :(
Thank you for this. Huge help and I love your enthusiasm!
I'm learning pre-calc before I go into calc next year and videos like yours are amazing! Your explanation and work is very easy to follow and so crip! Thank you so much and I'm subscribed!
Quem veio aqui pelo CEDERJ? RS
Thanks a lot. Great explaining, clear simple and direct!
7:45 i like how he calls them "everyone" i am just laughing at this for uncertain reason
Mais um inscrito. I'm from Brazil! Very good, congrats!
Thank you sir
Your teaching method is very nice👌👌
Thank you this, oh Great Wizard. This was very helpful!
you are proving maths is very easier for everyone
wow, ur so amazing sir! big thumbs up for u! God bless
U teaching style just amaze ty sir for this vedio
Amazing sir... Thanks for making this question so easy...
Good Class Sir ,
From INDIA
Hey bro, nice video!
Thank you I'm going to use this in my code
Wow, I really enjoyed this method.
If
1 + 2 + ... + n = (n(n+1))/2
and
1^3 + 2^3 + ... + n^3 = ( (n(n+1))/2)^2
does that imply that
(1 + 2 + ... + n)^2 = 1^3 + 2^3 + ... + n^3 ?????
Wow, that’s a really good observation.
does not imply, because ^2 is opposite root of the number. I think
Yes it is true
Thats the thing which he explained lmao ... just you need to know that
1+2+3+4+5+...+n= n(n+1)/2
And there is a beautiful way to derive this above formula without any derivation or integration or higher mathematics!
HELLO WHAT AN AWESOME EXPLANATION THANK U
When taking the k^2 the other side, where is the cub for (k+1) disappearing from
this is so goooooold! thank you so much!
why do you drop the ^3 after turning (k+1)^3 into (4(k+1)^3)/4 ???
I didn't get that either
Thank you brother Or more videos shar brother
Thx so much guy, but where are you from?
Nicely done sir..respects
Lol our teacher gives us only the left side and we have to figure what the right side is on our own, makes things a lot more interesting😂
You either have to already know the formula or test it and figure it out on the spot. Nice video!
Thank you so much! Only because of you I understood how to proof this!!!!
Thank you so much sir!!!
The last part is really useful and interesting!!!!
no entendi un choto lo que dijiste pero entendi el ejercicio que es lo importante jajaj like
Mira donde te vengo a encontrar JAJAJAJA
@@joaquinrivero7864 jajjaja pibeee
the way he says "i can do this"😂😂😂😂
000
thank you king. wish you were my teacher
I just started with mathematical induction and you make it so easy for me 😘
Thank you sooooo much ❤
Can you prove this without induction and instead with combinatorics?
So what it's greatest positive integer
Nice video.
this was brilliant
Oh Wow thanks really useful
That was awesome thank you guys
Thank you so much!
Can u make more vide in inductions please
Can you use induction the derrive a formula, or can you only prove one works?
Yoav Shati usually you use a different technique to find the formulas. Induction is a technique for proof more than derivation.
Awesome video. It really put things into perspective. I have one problem though. I usually find a hard time to form the conjecture of the series. Like for instance, how did you get {n(n+1)}/2. I usually find a hard time figuring it out. Any help will be appreciated.
Thank you
From morroco😍
Thank you sir from India 🇮🇳
Lovely , well explained
What's in your hand ??
Easy to understand thank you very much ...👍🏻I can pick up very much fast👌🏼 thank you very much again 🙂
Thank you!
how can in the end of solution, 4k +4 is not having power of three
Thank you very much.
You explained it very well.
Can someone explain the factoring at 6:15
what's confusing you? collecting the common (k+1)^2 terms, the fractions, or factoring k^2 + 4k + 4?
Thank u so much💜
Thank you soo much Sir
Is this possible without induction ?
Put the shaded box aaaayyyyyaaaaaaa
Suppose if it is 1power n plus and 2 power n and so on 15 power n what is the formula
Very useful thank you 🙏
Thank u , thank u very much .
Sir i boldly request u to post the easily proof of taylor series expansion from mean value theorem.
But if tou DODNT KNOW THE FORMULA HOWNWPULD DEDUCE IT??
Nice one explanation sir
Legends watch one day before the exam 😂
Can you do a video on why A^2 + B^2 = C^4 has no solutions in positive integers? Maybe it is really obvious, I don't know.
He can't because it's not true. For example, 60, 80 and 10 for A, B and C respectively is a solution in positive integers.
Take (a+bi)^4 this will give you and infinite list of values that will solve the equation where the real part is one leg, the imaginary part is the other leg, and the hypotenuse is the length.
5^4=(24)^2+7^2
is a counter example there are many counter examples u can generate them by using euclids formula consider (2mn, m^2-n^2, m^2+n^2) we want m^2+n^2=C^2 hence get another pythagorean triplet in form(m, n, C) plug it in to get A and B and you have it
Very good!
Entendi melhor em Inglês do que em Português.
THANKS!
Can you tell us how to build the formulas?
alternative proof : Start with n^4 - (n-1)^4 and simply it...
where the ^3 go
factorization
I am from india tamilnadu and studying this in eleventh maths ex4.4 first sum
but it is only true if ur inductive hypothesis is true...
but you just assumed ur inductive hypothesis to be true, can u please explain that a little?
Nice
thank you so much!!!!
Hi , can you do this :
Log1000(1001) vs log999(1000)
Thank you!
Lovely!
I am from india but I currently watching this
Nice ❤
I dont get it from 6:,30
شرح رائع احسنت
Thank you 😍
Спасибо !
Thank you ,I finally unferstand!
gracias... pude entenderlo ...😎😎✌✌
Very nice video
why n=k and next step n=k+1???
you do that everytime to prove that it works for all k
1+2/3+4
Nice vid, you're funny :D