why does 1+1/2+1/3+... = infinity?

[@ErtosAcc]

Very clean proof. Basically relies on the fact that if something is bigger than infinity, then it must be infinity. Really nice.

[@noreigaoconnorspecialk6771]

Sir...that is not a fact! # infinity as a point vs infinity as an incomplete approach! As a point, remember that zero is greater than infinity!

[@AlexandrePorto]

However, is it a fact?

[@violintegral]

By the way, it was Nicole Oremse who first used this comparison to show the divergence of the harmonic series. As a sidenote, I think this simple proof of the divergence of the harmonic series would be great to introduce the comparison test to a Calculus 2 class.

[@OrigamiCL]

That's what my Calculus II prof did! Really nice and neat illustration of the concept.

[@MikehMike01]

smart dude

[@Benzil_infinity]

Legends say that he's still holding that pokeball.

[@fuscello]

I haven’t even studied series + the semi language barrier (I’m Italian, so I don’t understand every single mathematical term), but still you make these videos clear and fun to watch

[@pablorodriguez7052]

happened the same to me at beggining (I'm spanish) but after watching many videos you learn all this type of words. You will get used to it, keep learning! :)

[@gabs1400]

Che bello un'italiano/a, buon Natale 🎄

[@manu_j_]

@@gabs1400 Buon Natale passato a tutti voi guys

[@logistaur]

Man this was such a nice video, a good memeoy refreshment And you can tell that you are very excited about it/sharing your knowledge in a simple way. You would make a great math teacher

[@bprpcalculusbasics]

Thanks. I am actually a math teacher. 😃

[@RaceCmart]

Let's just appriciate the pokemon thingy in his hand, he was holding it for entire video. Great power. Infinity out of infinity

[@iexisted583]

Pokeball*

[@ggmxz]

@@iexisted583 I think it's his microphone, you can see a cable going down from the pokeball.

[@taterpun6211]

@@ggmxz he’s just charging the pokéball

[@yelnatspowerzz4970]

From 2:45 to 5:45 makes the most sense. Example u will eventually get to 1/8 which is .125 by the time u add up all of the numbers before 1/8 u will get a number of .5 or greater which means by the time u hit 1/8 u get +.5 then same when u hit 1/16 u will have another .5 by then, yet again with 1/32 another .5 essentially always giving you +.5+.5+.5 eventually getting you to infinity

[@muzankibutsuji5572]

we can use ln(1+x) expansion ln(1+x)=x-x^2/2+x^3/3-x^4/4 ln(1-x)=-(x+x^2/2+x^3/3....) putting x=1 ln0=-(1+1/2...) -infinity=-(1+1/2...)

[@UnknownGhost97]

Ln 0 is not defined [not infinity ]

[@Ninja20704]

very useful. I also watched eddie woo and khan academy doing the same proof, but i feel yours was the most helpful as it shows why u choose the powers of 2 for the denominator

[@thebattlebarley2308]

Please how can I use this in real life? (I'm not being impolite, just curious how can I use it useful)

[@Iamcookeddd]

You can't my guy

[@tarehjernetarehjerne4082]

I really do not like khan academy. Say when they showed derivation, they used e^x. Its like they purposely try to teach as little as possible

[@pi6141]

@@thebattlebarley2308 You can't really "use" it. I suppose it is certainly entertaining to learn about, and it might help you improve your critical thinking skills, but other than that you won't be using these anywhere besides showing it to your friends. The application of problems like these is simply that it contributes to developing mathematic, which is the fundamental subject to then develop computer science, physics, etc. So if you're not pursuing a career in these fields you might find it pretty useless.

[@thebattlebarley2308]

@@pi6141 OK thanks for explaining :)

[@Scryllix]

This is the first video I've seen from you an d i already know I'll be watching more! That was really interesting

[@iCalculatorInfo]

I saw my math teacher with a piece of graph paper yesterday. I think he must be plotting something.

[@gustafbstrom]

Thanks, love your pedagogy. Keep up the good work!

[@bprpcalculusbasics]

Thank you

[@sergioh5515]

Wasn't aware of this classic proof! But so far I love it! Beautiful

[@tanishqk9826]

The cookie example was great 💯

[@bprpcalculusbasics]

Thanks 😊

[@JulianShagworthy]

Imagine you walk 10 metres, but split it into sections, the first section being 5 metres, then every subsequent section being 1/4 the length of the previous one. No matter how many times you apply this, you'd never reach 10 metres. But you do. So you've surpassed an infinite number of sections by walking ten metres :)

[@odobenusrosmarus6035]

no you wouldn't reach 10 meters. the geometric series with first term 5 and common ratio 1/4 approaches 6.66.. meters, so you'd only reach 6.66..

[@-YELDAH]

i think i saw a video on this topic, you are obviously just defining something in a way that isn't true

[@gtgagaggagagagga]

(1/2)^n doesnt diverge though so u dont get to infinity.

[@antro_phagus]

I stumbled upon this video by mere chance, as I never watch math related content I was pretty much expecting not to understand anything... but, I was able to follow along for the entire video, and it really turned out to be very interesting! Your explanation is amazing, and it genuinely made me enjoy math even if I'm rarely good at it Thanks so much for sharing! This is a very cool video

[@michaelthedude8009]

same litterally same

[@bprpcalculusbasics]

: ))))

[@michaelthedude8009]

@@bprpcalculusbasics :)))))

[@createyourownfuture5410]

@@bprpcalculusbasics : )))))) Please repeat this... I have 6)'s, so do 7 next. Edit: Thank you Faast -Mathematician- man!

[@iDontProgramInCpp]

@@bprpcalculusbasics : )))))))

[@SmokeyMagma]

Very good video, especially now with calculus 2 in the spring semester!

[@bprpcalculusbasics]

Thanks!

[@Ventoaurelion]

Clean as always. Good job

[@bprpcalculusbasics]

Thanks.

[@mikejackson19828]

I love your videos Steve! Keep up the good work mate! 👍👍👍

[@bprpcalculusbasics]

Thanks!!

[@danielevilone]

I would simply notice that the sum S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +... if we assume it finite must be strictly larger than the sum S' = 1/2 + 1/2 + 1/4 + 1/4 + 1/6 + 1/6 +... (where we substituted each odd terms with the next one): S > S'. But it is easy also to see that S' = S ==> contradiction.

[@anonymouscheesepie3768]

The integral of 1/x from x = 1 to infinity also diverges. You can show graphically that the sum of 1/n from n = 1 to infinity must be greater than the area under 1/x from 1 to infinity. Since the infinite sum of the reciprocal natural numbers is greater than the area under 1/x to infinity, and the area under 1/x to infinity diverges, said sum must also diverge.

[@mangss9602]

This guy is a genius

[@c6h12o6-y3p]

あきとんとんさんの1-2の深読み計算から来ました。無限級数の考え方に腑に落ちました。 Thanks to your expression, I was able to find out the way I consider limit. I was surprised at this thoght, area of square.

[@SnailMan63]

I don’t even take calculus anymore but this is sick

[@dimasveliz6745]

I knew about the sum of inverted powers of two being equal to two, but this divergent sum proof using the prior one was astonishing! Awesome video

[@canismajoris6061]

In some infinite sequences, when there is nothing left, the answer is a natural number. But if there is anything left, the answer is infinity. when you start collecting from the first series : if the first selection is 1/2, that means it's empty as well as 1/2. And if the second selection is 1/3, then the free zone is (1/2 -1/3) ..So 1/6 ..But the third choice is 1 /4 closes the gap..Because 1/4 >1/6 ..So that the next selections cannot stay inside the square and they overflow..So this series goes to infinity..

[@mikael9325]

cool, didn't think about it in that way

[@canismajoris6061]

@@mikael9325 İn the end one sent a msg -_-

[@mikael9325]

@@canismajoris6061 ?

[@ankitthakurankit4764]

5:43 the second line you are using inequality (>) but in 3rd line you are using equal(=) please explain.

[@dunemeister5718]

Remember having my mind blown when I saw this in one of my analysis lectures, epic proof

[@crep50]

I’m gonna do some notes before I watch further in the video (2:31 is where I’m at) The top one has to converge to a number larger than 2, as it contains 1* (“N*” meaning N if done infinitely) If I’m not wrong, I’m Thinking that 1/3 + 1/9 + 1/27 + ••• converges to 2/3? Just a rough guess though, please correct me if I’m wrong (and if the video doesn’t correct me first)

[@crep50]

Aight so I mean, it was certainly larger than two 😅

[@ImaginaryHuman072889]

makes sense on paper, still strange to think that you can add infinitely many numbers that keep getting smaller and it diverges

[@thomasschneller7081]

What would stop you from adding any latter elements of a convergent sequence and proving it’s a divergent series? Couldn’t we do the same for 1/n^2

[@ijneb1248]

Basically its because 2^n will grow faster than n^2 so when you round up the n^2 terms to the 2^n term smaller than them theyre gonna grow smaller and smaller and wont ever get past 2 like the example he showed at the end

[@thomasschneller7081]

Okay thanks. I think I got it. It’s gonna take a while to wrap my head around this.

[@thomasschneller7081]

Yep, I see it now.

[@Experiment626-1]

i literally have no idea how to calculus but this video is still very cool

[@noahbody9782]

How about a geometric visualisation of the divergent series?

[@jasonmuring7434]

Hi, tried something differently like increasing all odd denominators by 1 (say 1 becomes 1/2, 1/3 becomes 1/4, and so on.). This should make the original series greater than the new series. However, the series comes out exactly the same. See below. O = 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+... N = 1/2+1/2+1/4+1/4+1/6+1/6+1/8+1/8+... O > N (right?) But, N = 1+1/2+1/3+1/4+... Therefore, O = N So I'm confuse, what makes it oddly wrong?

[@abhikigaming3261]

Wtf......

[@s888r]

Guy: Teaches mathematics Guy: *Holds Pokeball*

[@reav3rtm]

I'm too dumb for this. How come 1 + 1/2 + 1/4 + ... = 2? It approaches 2 (lim) but I think it will always lack that infinite small 1/inf piece to be 2 and will be smaller than 2. I don't get that.. And if so, how can it be used on the right hand side in the proof and that that almost 2 is big enough to tip the scales of 1 + 1/2 + 1/3 + ... to approach infinity. Is finite lim value in mathematics arithmetically equal to finite number?

[@rubixtheslime]

First infinite sums are in essence a limit, as they approach something and you can't add infinitely many numbers. And the other part is you can think of limit being a function that says "whatever this approaches, that's what I equal." So if xyz approaches 4, then limit(xyz) _equals_ 4. But good on you for realizing that, most people trip up for _not_ knowing that approach and equal are different. As for the other part, (assuming we're in the same page) it's a whole new sum at that point, he's basically saying that if we replace some of these with something smaller but it still diverges, the original diverges as well. So replace 1/3 with 1/4 because 1/4

[@reav3rtm]

@@rubixtheslime Thanks. I have not refreshed my math for 15 years so obvious things to others may not be immediately obvious for me. I did follow his proof method and I thought I understand it. And I did in fact but my reply above showed I didn't, as I suggested he did something he in fact didn't do. Which is using 1 + ... + 1/2^n to prove 1 + ... + 1/n is divergent. What confused me was his omission of lim or -> (he put =, though he did say 'converges' initially but later said equals or is 2) and that he brought 1 + ... + 1/2^n -> 2, even with graphical representation, without - I understand it only now - actually using it in his main proof. Because his primary trick to prove 1 + ... + 1/n is divergent was replacing fractions with smaller fractions just to be able to easily group them in infinite sequence of ones. And bringing that other sequence (with lim = 2) and omissions of lim symbol just obfuscated it all for me.

[@Frownlandia]

Here's a question related to this proof in a sideways kind of way: If the harmonic series is analogous to zeta(1) (Riemann zeta function, obv.), and that diverges, is there a point in the zeta function analogous to the smaller sum in this proof?

[@skylardeslypere9909]

What do you mean with your Last question?

[@dlevi67]

Not really - the Zeta function is defined as the sum of the reciprocals of powers of natural numbers (the exponent being the independent variable); no base is repeated. You can write a formal expression for the other series using e.g. the floor or ceiling function to have the powers of 2 appearing multiple times, but that's not a point in the Riemann Zeta function.

[@maxboku]

Well, the domain of the Riemann Zeta function does not include Zeta(1) or Zeta(1+yi) so you can't really use it in the way you talk about.

[@sergioh5515]

Hi Steve, just found this other channel. Just subbed as well. I'm looking forward to watching you again! And all throughout the year. Keep up the good work! So far I'm liking this video and this is my first one I'm watching on this channel 😊

[@bprpcalculusbasics]

Thank you Sergio! Hope all is well and happy new year!

[@natanaelblomberg2286]

Damn, this is sooo satisfying. Just showed this to all of my family members. Unfortunately they couldn't care less :(

[@SkyTheHusky]

Isn't 1+1/2+1/4+1/8...1/(2^a) less than 2? I mean, if you draw a circle, then half a circle, then quarter a circle, will it ever add up to 2 circles?

[@elilogan8630]

Lim as a -> inf is 2

[@jimhunt2283]

if you do it forever and ever and ever and ever then it will hit 2, when you have added infinite terms.

[@SL-gz9gq]

It’s exactly two I believe

[@Maxodex]

it will never add up to 2 if you only do a finite amount of sums, but when you do it infinitely then it is exactly 2

[@SkyTheHusky]

Idk i'm in 5th grade

[@i.i]

I can believe everything after 1+2+3+4.... =-1/12

[@maxboku]

The Riemann Zeta function just slaps logic in the face lol when it says this.

[@mafarbait4424]

But im wondering where the 1/3 and other none 1/(two exponent) number go on the part that it's equal to 2?

[@abhikigaming3261]

Exactly

[@noreigaoconnorspecialk6771]

Whats the summation equation for 1 + 1/2 + 1/4 + 1/8.... again? Is it sigma between n=0 and n=infinity for 1/2^n ? 🤔

[@kedwinhawkins9930]

as a 7th grader that clicked on his video to try to understand this my mind is blown away i do not understand much

[@teknul89]

It never ends man it just keep going on and on and on two infinity and beyond

[@liljod2894]

Another proof we can do is actually take 1/n + 1/n².... And do this series till infinity u will get finite numbers adding to infinity so is it equal to -1/12??

[@muudip9151]

After a while i got it, by making some of the numbers in the series smaller, make so the numbers can be united in groups that would equal to 1/2, and since the series are infinte, there are infinitelly many 0,5 or 1/2, and adding those will go(*)to infinite, so because a smaller series goes(*) to infinite then the larger one by logic should equal to infinite too, it just goes(*) to infinity at a faster rate Sorry if i made any mistakes english is not my fisrt language but i think the point will get across (*): i don't like saying it equals to infinite since infinite is not a number, but i guess it means the same

[@orenfivel6247]

can you proof PLS that harmonic's partial sum is squeezed between two logarithmic functions without integration?

[@felixnotkjellberg]

Me who watched similar questions before and still forget how to solve

[@randomjin9392]

bprp writes *Pf:* Me: +10 points of coolness! bprm writes *= ∞* Me: -50 points of coolness :p

[@robertveith6383]

"bprm!?" He is blackpenredpen.

[@violintegral]

Actually, writing something "equals infinity" is justified in some contexts. It depends on which number system you are using. For example, the extended real number system adds two elements to the the familiar real number system: +∞ and -∞. Use of this system allows us to say that a limit equals infinity, or has a value at infinity.

[@helloitsme7553]

It's just notation he doesn't actually mean the limit is equal to infinity

[@oscarfoley511]

@@renderize69 he did mess up the spelling once actually

[@renderize69]

@@oscarfoley511 check up the comment, it's not edited!

[@chibrax_zt5903]

What a great video, thanks for this moment

[@avi_here]

Well, but as the fractions are approaching 1 or are arbitrary close to 1. So, if we add the remaining number that is no.1 in it the answer comes as two. Because the more larger the denominator gets the smaller the value. Therefore the answer must be 2.

[@gtgagaggagagagga]

No, u get over 2. U get 2 if u calculate 1+1/2+1/4+1/8+... where u have less things to calculate.

[@paulnelson8419]

I like how hes just holding a pokemon ball plushy the entire time lol

[@bprpcalculusbasics]

Thanks!

[@pierineri]

to be precise, you should use a ≥ sign, not >. Inequalities and arithmetics in the extended real line are perfectly meaningful, but there from 1/3 > 1/4 you can only deduce x+1/3 ≥ x+1/4.

[@jannikhilger6739]

Never expected me to find this out ba myself

[@bgmarshall]

I did a simple thing of code that can run this formula until either n or the answer reaches some amount and it starts going really slowly after the answer is like 10. Just going from 11 to 11.1 takes 3535 times of adding 1/n + 1/(n+1).... All the amounts running it until the answer is 12 is as follows. The first number will be how many of them there are and the second will be what the whole number part it 3 1 7 2 20 3 52 4 144 5 389 6 1058 7 2876 8 7817 9 21247 10 57757 11

[@bgmarshall]

If you want to copy past the code for some reason it is (this is in c++) #include #include int main() { double n = 1; double answer = 0; // you can do n instead of answer for the while statement, and you can change what it's < while (answer < 11) { answer = 1/n + answer; std::cout

[@bgmarshall]

if you want to count the lines like I did just do ctrl + f then in that space put "is (whatever you want to count, this can be nothing if you just want to count the lines)"

[@PennyLapin]

Would this be a proper way to phrase the final "1 + 1/2 + 1/2 + 1/2 + ..."? "We can write this repeated sum as: = 1 + [lim_{n -> ∞} 1/2 * n] As n goes to infinity, the 'times one-half' becomes trivial and we are left with n being infinite, therefore this limit is unbounded. Since our one plus repeating one-halves sum is unbounded and goes to infinity, we know that the harmonic series, which is greater than our sum, also goes to infinity."

[@April-xl1ht]

My mind is blown 🤯🤯🤯 Also, I'm curious,why do you always carry a pokeball? And why do I love it xD

[@bprpcalculusbasics]

It’s a mic.

[@April-xl1ht]

@@bprpcalculusbasics Well it's the best mic I've ever seen

[@trishan6992]

How can we determine the sum of this series for 1+1/2+1/3+...1/n

[@glennbaker7914]

Logic tells us we are adding smaller and ever smaller bits to the total as we increase the length of the series. So we must meet some limeted quantity. Perhaps normal logic is void when considering infinity.

[@venkybabu8140]

Breakdown into two series. 2 and one over 3 and one over 2. So 4×3 12.

[@enescoskun0123]

That was clean 💯

[@tekiic6680]

i don’t understand a thing but this is cool

[@spinningforever119]

But I mean if you keep continuing you should normally get a number that’s under than 2 cause you keep adding numbers smaller than 1 in a way where it won’t reach the next number and also the note you did where it’s 1+1/2 +1/4 +1/8+1/16 it’s not 2 it’s 31/16 so it hasn’t reached 2 so that means even if they continue they won’t reach 2 I just want to understand not saying it’s wrong

[@gtgagaggagagagga]

It tends to 2, so if u do it infinity times you get 2.

[@dandancaster6914]

this division in real life cannot go on forever specially in subatomic particles, I don't know but like an electron or quark there must be a last particle which cannot be splitted the real end in phisics, it must be extremely tiny much tiny than string particles

[@walker3560]

Bro I think we all know. He was just explaining it in a simpler way.

[@twosomestars9254]

The point is that number never ends :(( and we know that size of any physical object can be infinitely small. Right now we magnify surface to see molecules then atoms and we got to conclusion about smallest things such as electrons or quark..But we don't know what new thing will emerge on magnifying quark. There are infinite small things..

[@dandancaster6914]

@@twosomestars9254 size of any object CANNOT be INFINITELY small,this is my argument,while numbers go on,matter does NOT

[@twosomestars9254]

@@dandancaster6914 But you need numbers to represent size, and size include dimensions such as length, breadth... which can be infinitely small units since numbers can be infinitely small too..

[@KaliFissure]

Consider any world path. Ones life for instance... your fist year, this first year is the entirety of your life. But your second year will only represent half of your life and your third year of life is a third of your life...etc.

[@abiyyuyandra1065]

Now i got the point. Convergence sequence divergence series

[@MarcatoCSharp]

How can the 1+1/2+1/4+1/8... thing equal 2. The cookie example makes no sense to me because you would have to double the value eventually to have the cookie be whole. Wouldn't it be equal to 2-1/infinity then? Because it will always be missing that last piece

[@samabudhabi1370]

You got confused bc the cookie example he showed proofs focuses on 1/2 +1/4+.... = 1. The better analogy would be if he had drawn two square cookies. Imagine you eat one whole square cooky on day 1. Than you eat half of the second square cookie on day two etc....if you keep doing that for infinity you will never have eaten more that 2 cookies.

[@somekid39]

If you assume it is less than 2, say some number x

[@MarcatoCSharp]

@@somekid39 ok this makes a lot more sense. Thank you for taking the time to teach me!

[@somekid39]

@@MarcatoCSharp :)

[@bprpcalculusbasics]

I love when good discussions happen in the comment section! Great job everyone!

[@WolverineIncognito]

This actually triggered my ASMR!

[@Vickyy__.]

What is the answer of 1+ 1\2 plz. Tell me. The answer

[@honkadaloonga7046]

Unrelated to the video, but is it possible to compute the exact value of the area enclosed by x^2 and sin(x)? Wolfram Alpha doesn't seem to be able to give anything more than a numerical answer. Thanks

[@jopetdevera]

It's pretty hard to solve x^2 = sin(x) analytically so probably that's why. I think it can only be solved numerically.

[@rubixtheslime]

@@jopetdevera naw it's super easy just replace sin x with x everyone knows that's a 1to1 substitution it happens at 1 lol

[@flamevenomspider]

On a graphing calculator: graph both, find the intersection (around x=.877), and integrate (sinx -x^2) from 0 to .877

[@Inspirator_AG112]

Replace every divisor with the exponent of 2 just above it.

[@chesterlai9444]

I was kind of thinking that because 1/ the powers of 2 that and that there are a infinite amount of positive interger I can reason since 1/ the powers of all positive intergers would combine Into infinity because of course 1/ all positive interger powers = a finished number

[@Be.quentin]

After 5 :36 I finally noticed that he had a pokeball during the whole video

[@Cube_Box]

cool video but why r u holding a pokeball

[@Giniro_No_Suisei]

Indeterminate form?

[@kenbrady119]

You cannot keep cutting that cookie! Even if it were a big cookie (1 meter x 1 meter), after ~116 days, you will be down the the Planck length, and the cutting must stop.

[@xinpingdonohoe3978]

Which is why maths occurs in the idealised physics world, where Planck values are only a suggestion, matter starts uniformly distributed and resistance to motion is a side dish that you could just reject.

[@Shreyas_Jaiswal]

Yes, assume a cylindrical cow in vacuum. 😀

[@neilgerace355]

@@Shreyas_Jaiswal spherical: fewer degrees of freedom :)

[@anairoatapea9055]

Quand n tend vers l'infini la limite egale à 0 donc au final ça fera 1

[@andrewmk8514]

Can someone please explain the pokemon ball?

[@oenrn]

"1/3 is bigger than 1/4" Americans who rejected the third-pounder burger because they thought it was smaller than a quarter-pounder: visible confusion.

[@AsifIkbalMondalees]

very nice sir.

[@alexdacat7052]

But 1 1 5 1 + - + - just equals 1 - though 2 3 6

[@alexdacat7052]

Just change them into sixths so you can combine them

[@alexlo7708]

By human senses . That made me feel contrast. One summation goes to infinity while other has its exact value.

[@ClockBestEvent]

Good video!

[@josidemo]

1+1/2+1/4+1/8+1/16+..... not equal to 2. An integer (or any number) can always be halved, infinitely. Nothing precludes it from being possible. I also have proof for this particular case. The result of this series can be calculated: x = 2-2 / infinity.

[@gtgagaggagagagga]

Series n goes from 1 to inf (1/2)^n is in fact 1. And 1+1 is 2

[@josidemo]

@@gtgagaggagagagga 1/2 + 1/4 + 1/8 + 1/16 + ... will never be 1. There is no number so small that it cannot be halved, just as there is no number that cannot be doubled.

[@rubixtheslime]

1:40 yeah I think I got this, next is 1/16, then 1/31...

[@WhyDoesMyCodeNotCompile]

A nice simple proof

[@petereziagor4604]

Okay, cut it by half until you have nothing to eat

[@edwardsicily]

You will always have something to eat! As the days goes on you will always have less but it will never be 0. Of course your gonna end starving eventually 😂

[@Sam-mb5zf]

1 + 3/6 + 2/6 = 1 5/6?? Edit: nvm it wasn't just 1 + 1/2 + 1/3 It's that but continued on into + 1/4 + 1/5 + and so on.

[@keerthisri4499]

hi i am rakshith im in class 7 i have a doubt in finding how 1 cubed +2 cubed +3 cubed +......=1/120

[@Drachenherz1901]

Actually clicked on this video because i wanted to know why the math guy is holding a freaking pokeball

[@yoav613]

Dear bprp,can you please make avideo about why (0)^(a+bi)=0 when a>0,but 0^(bi) is not defined? (At least that what wolfram say)

[@dlevi67]

One simple "intuitive" reason is that if you consider x^(a+bi), for real x, a, b, x 0, this expression has absolute value (modulus) x^a. Adding an imaginary part to the exponent has the effect of taking the modulus and 'rotating' it around the origin. 0^0 is undefined (both base and exponent real); if the modulus is undefined, its rotation is undefined too.

[@davidbrisbane7206]

This proof in this video was first proposed by Nicole Oresme around 1350.

[@alexpsallidakis28]

Knows math ✔️ Speaks good English ✔️ Likes Pokémon ✔️ Has a cool beard✔️

[@faydo2787]

I'm confused. How does 1+1/2+1/4+1/8...= 2? Every next addition is always only half of what it would take to get reach another whole, how could it ever reach 2?

[@FranciscoFloresNyu]

He explained that

[@faydo2787]

@@FranciscoFloresNyu When? Sorry if I missed it but I heard him say since there infinite of them it eventually reaches 2 which still doesn't make sense to me

[@FranciscoFloresNyu]

@@faydo2787 He explained with a cookie, how cutting in half a piece each time, you go 1/2, 1/4, 1/8, 1/16, ... infinitely, and it's still one cookie. So 1/2 + 1/4 + 1/8 + 1/16 = 1. Then add the single 1

[@faydo2787]

@@FranciscoFloresNyu Still doesn't make sense to me. It's one cookie but idk how you end up actually cutting the whole cookie if you always cut only 50% of what would it take to reach the full cookie. Having infinite steps just makes it so there's an infinite number of times you only go half the rest of the way. So seems like there'd be an infinitely small space between what you've cut and the whole cookie, but still a space no? Not trying to debate btw I just want my doubts addressed

[@FranciscoFloresNyu]

@@faydo2787 I now understand what you mean. If you do the calculations manually, it will never reach 2, no matter how large is N. For this you need to understand the concept of limits, series and infinity. For that function, the value approaches 2, as n goes to infinity. It never surpasses 2. So mathematically you can say that the whole serie = 2

[@SuperYoonHo]

subbed !

[@airatvaliullin8420]

'pf' is good and stuff, but I like the □ ■ more :)

[@kashyapchothani9737]

Amazing👏👏

[@GammaZ]

I think the only reason this vid is on my recommended is because youre holding a pokeball lol

[@xinpingdonohoe3978]

Did you learn something though?

[@bprpcalculusbasics]

😆

[@violintegral]

What I learned from this video is that I should only eat 1/2 of what's left of my cookie every day so it will last forever. Of course, it'll probably get moldy and stale, but it will be worth it to really savor the cookie.

[@bprpcalculusbasics]

😆

[@vojtechsejkora1554]

unfortunatelly you cannot divide electrons. But otherwise good idea :-).

[@mskyba]

After like a week the pieces will be too small to enjoy, but a similar strategy in the same spirit would be to split it up into small pieces at the start and eat one each day. The key is to make the pieces just big enough to be still enjoyable

[@Tealen]

lmao