Prove by induction, Sum of the first n cubes, 1^3+2^3+3^3+...+n^3

[@lukaspfalz6128]

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"

[@jemcel0397]

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.)

[@adirmiller2141]

cozy, for me its a fire bit of hell

[@imperialrecker7111]

I proved the differentiation from first principles with induction. it was really challenging

[@sheetalsorout5637]

Yeah it's true

[@Aaron-hh8nx]

It's not cozy for me

[@ARN48411]

Yes

[@anzhelakryzhanovskaya849]

Я, русскоязычная казахстанка, ничего не понимающая в английском, сижу разбираю тему в интернете, чтобы объяснить её своему ребенку. Спасибо за Ваш труд.

[@Iucebowel]

(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

[@derrickwright1701]

Your explanation is amazing. Succinct and detailed at the same time 🙏🏾

[@OllieWalle13]

You just connected so many things in my brain. Thank you so so much

[@akshat9282]

10^5 congratulations!!

[@sugarfrosted2005]

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.

[@MathForLife]

I love math induction! Super useful:D

[@trentconley4374]

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!

[@MrAleguerreiro]

what does the box at the end means? is it just like Q.E.D.?

[@blackpenredpen]

Yes.

[@EghbalSeydi]

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

[@shuilin1499]

wow! 曹老师让我第一次学会了这么强大的功能！

[@rehamabdul-karim6281]

I just loved your spirit, energy and the way you are explaining things!! I wish you were my instructor instead :(

[@deathwildrift3225]

Mais um inscrito. I'm from Brazil! Very good, congrats!

[@shilpareddy9674]

I just started with mathematical induction and you make it so easy for me 😘 Thank you sooooo much ❤

[@DcMag]

Quem veio aqui pelo CEDERJ? RS Thanks a lot. Great explaining, clear simple and direct!

[@MrsEvans-es2fo]

Thank you for this. Huge help and I love your enthusiasm!

[@KwongBaby]

Great teacher. i love maths

[@blackpenredpen]

Baby Kwong thank you

[@amanpreetkaur2748]

Thank you sir Your teaching method is very nice👌👌

[@saythealphabet776]

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!

[@mitchellcampbell2775]

Thank you this, oh Great Wizard. This was very helpful!

[@kakashisensei6358]

You are such a good Teacher

[@rasmitabiswal1014]

U teaching style just amaze ty sir for this vedio

[@doyourbest9541]

Amazing sir... Thanks for making this question so easy...

[@friedrichfermi6559]

7:45 i like how he calls them "everyone" i am just laughing at this for uncertain reason

[@suvalinandy7088]

Thank you so much sir!!! The last part is really useful and interesting!!!!

[@nandhinis1542]

Easy to understand thank you very much ...👍🏻I can pick up very much fast👌🏼 thank you very much again 🙂

[@jaredmartin2003]

I like your enthusiasm at the end.

[@marcinkuleta8264]

Wow, I really enjoyed this method.

[@weirdyyy006]

Thank you so much! Only because of you I understood how to proof this!!!!

[@lheanmargarico9552]

wow, ur so amazing sir! big thumbs up for u! God bless

[@pandikalai7695]

you are proving maths is very easier for everyone

[@huzaifabid3047]

Nicely done sir..respects

[@chesapeakecharles615]

why do you drop the ^3 after turning (k+1)^3 into (4(k+1)^3)/4 ???

[@micaelaarslanian8629]

I didn't get that either

[@Super-Super-Man]

Hey bro, nice video!

[@dzikrasyafitri]

this is so goooooold! thank you so much!

[@akshay164]

Good Class Sir , From INDIA

[@shoukathali1768]

the way he says "i can do this"😂😂😂😂 000

[@aousdalloul9402]

Thx so much guy, but where are you from?

[@thebrownintheblack8835]

Thank you I'm going to use this in my code

[@paulphyo]

HELLO WHAT AN AWESOME EXPLANATION THANK U

[@Ch1pp007]

Nice video.

[@shivam6450]

Thank you very much. You explained it very well.

[@franzsenkelo6246]

When taking the k^2 the other side, where is the cub for (k+1) disappearing from

[@nicolasmayorga8288]

Oh Wow thanks really useful

[@kylewitha_c308]

Can you prove this without induction and instead with combinatorics?

[@beezball38]

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 ?????

[@leadnitrate2194]

Wow, that’s a really good observation.

[@lucassantos6272]

does not imply, because ^2 is opposite root of the number. I think

[@lloydmace3546]

Yes it is true

[@usemymemefornoreason3215]

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!

[@amirzojaji482]

this was brilliant

[@j.m.butler5010]

thank you king. wish you were my teacher

[@lathashreelifestyle6584]

Thank you brother Or more videos shar brother

[@wisalelalouan7659]

Thank you From morroco😍

[@I_am_Signal]

Thank you!

[@shayanfatima2522]

Thank you so much!

[@yoavshati]

Can you use induction the derrive a formula, or can you only prove one works?

[@hedgechasing]

Yoav Shati usually you use a different technique to find the formulas. Induction is a technique for proof more than derivation.

[@vaniragujana]

Lovely , well explained

[@collinskariuki2586]

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.

[@pinkytae5069]

Thank u so much💜

[@kamalmakhloufi9484]

That was awesome thank you guys

[@Himricks]

Thank you sir from India 🇮🇳

[@chanchalsharma4230]

Thank u , thank u very much .

[@ayeshakhanayeshaayesha5764]

Thank you soo much Sir

[@tx7tarunff]

Nice ❤

[@vivekg8725]

Can u make more vide in inductions please

[@johnlucasdarling3606]

Very useful thank you 🙏

[@danieldesampaio]

Very good!

[@SHANTANUASHTEKAR]

What's in your hand ??

[@crashbandicoot2383]

Is this possible without induction ?

[@Kiran_playsYT]

Legends watch one day before the exam 😂

[@bautistamiguel5408]

no entendi un choto lo que dijiste pero entendi el ejercicio que es lo importante jajaj like

[@joaquinrivero7864]

Mira donde te vengo a encontrar JAJAJAJA

[@bautistamiguel5408]

@@joaquinrivero7864 jajjaja pibeee

[@timothykisembo8378]

So what it's greatest positive integer

[@thaisbeleza1634]

Entendi melhor em Inglês do que em Português. THANKS!

[@dreyashii]

thank you so much!!!!

[@nandhininagarajan7351]

Nice

[@Jeff_Segal]

Lovely!

[@rachidanj5276]

Thank you 😍

[@skytetpoint9916]

Nice one explanation sir

[@supratimsantra5413]

Sir i boldly request u to post the easily proof of taylor series expansion from mean value theorem.

[@vulcold3923]

how can in the end of solution, 4k +4 is not having power of three

[@nickma24]

[@avrilli9344]

Спасибо !

[@roopashree13]

Suppose if it is 1power n plus and 2 power n and so on 15 power n what is the formula

[@jakubfrei3757]

Nice vid, you're funny :D

[@aleksasekulic2133]

Very nice video

[@salomontontaquimba6535]

gracias... pude entenderlo ...😎😎✌✌

[@farzadsaeidi2120]

alternative proof : Start with n^4 - (n-1)^4 and simply it...

[@omarifady]

Hi , can you do this : Log1000(1001) vs log999(1000) Thank you!

[@Timorftw]

Can you tell us how to build the formulas?

[@leif1075]

But if tou DODNT KNOW THE FORMULA HOWNWPULD DEDUCE IT??

[@adamvozenilek3698]

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.

[@badrunna-im]

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.

[@thedoublehelix5661]

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.

[@sayantanmazumdar9371]

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

[@biistful]

Can someone explain the factoring at 6:15

[@CaradhrasAiguo49]

what's confusing you? collecting the common (k+1)^2 terms, the fractions, or factoring k^2 + 4k + 4?

[@antediluvianmono]

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?

[@namunamu3424]

شرح رائع احسنت

[@praseedkumar8373]

Thank u sir

[@josephsmart5258]

I am from india tamilnadu and studying this in eleventh maths ex4.4 first sum

[@zoyaaisyah6635]

Mantap kak

[@vivekg8725]

Put the shaded box aaaayyyyyaaaaaaa

[@Prem-KC_learner]

Thanks

[@cristhianivan6358]

you are good :D

[@szymonandrzejewski6087]

Thank you very much, you rescued me