Ramanujan Paradox | 1+2+3+4+....... = -1/12 | Aman Sir Maths

Ramanujan Paradox | 1+2+3+4+....... = -1/12 || Bhannat Maths | Aman Sir Maths
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[@abhishekkhulbe3905]

I just shocked to see that how the sum of all natural numbers is -1/12 . A humble salute to the one and only S. Ramanujan

[@dipikaghosh6224]

It's a paradox

[@silverfangg45]

@@dipikaghosh6224 string theory me lagta hai

[@Amit1994-g9i]

@@silverfangg45 nope

[@jayantsingh3078]

@@Amit1994-g9i In String theory it uses

[@binodtharu8348]

@@silverfangg45 agr string theory mei lgta hai to hm kya kre string theory is just a "theory" and i think u should google the meaning of "theory".......(i mean string theory is not like it could be 100 percent true)

[@techmaster6587]

"An equation for me has no meaning unless it expresses a thought of God!!" ~ *S. Ramanujan* ♥ *JAI NAMAGIRI THAYAR DEVI* 🚩♥

[@IIT24Aspirant]

So that's why he was so much interested in infinity equations?

[@techmaster6587]

@@IIT24Aspirant yepp!

[@cassianperera2426]

Ramanujan is a true genius in Mathematics, according to this statement mentioned by him.

[@jod5783]

Aa gaye gawar

[@cassianperera2426]

It is exactly true that the Ramanujan's statement.

[@sudhirkumar-kp5lc]

Ramanujan in one of his papers also dropped hints to form the equation of a black hole in one of his letters. It's crazy how much he would have contributed to mathematics had he been introduced to it earlier.

[@vinaykumarsingh6223]

The line " fat gyi thi .....aankhe logo ki"is just OP 😂😂😂😂😂

[@Southmovies509]

😂

[@DeepakKumar-iy1ck]

😂😂😂😂😂

[@SagarsAudioHub]

"Mathematicians होते ही साफ दिल के" 😀❤️🙏 Sir Ramanujan was the hero , is the hero and will be the hero 🙏 Big salute to him. And, your teaching is fabulous sir ji 💞

[@theharo4084]

Mathematician bolke illogical baat bhi bolrhe ho

[@hridayjoshi7247]

Meri bhua to nahi hai

[@cheapdealskabanda7709]

F

[@thegames4499]

kyu bhai tumhara knowledge jayada ho gaya hai kya kya tum ramanujan se zayada gyani ho

[@shouryashukla5817]

Well it was destined to be paradox, as the very first series 'A' is a paradox itself, as the sum of 1-1+1-1+1-1+1-1+...... Can be either 1 or 0 depending on the last quantity of the series, as it's till infinity it's unclear what is the last numeral, so the answer should be either 1 or 0, but, by solving this series i.e. by taking common we got 1/2, it's actually impossible, I think it's the average of 1 and 0, and we can't solve maths by taking a contradictory value and further assigning it, hence sum of all natural numbers was destined to be a paradox.

[@Supriyobiswas649]

Finally, someone who actually knows how math works.

[@lorex340]

kzbin.infoGfBXmTDz15E?feature=share

[@samarthgupta5981]

Exactly, well that's the beauty of infinity in such problems, we know something is there which is distorting the true value but we can never find it coz it's ♾️😂

[@indmh20shreyas42]

Yeah,if th no. of terms,if are even ,then the sum is 0 and if odd,then 1😊 well said ,bro!

[@ETM247]

Exactly

[@swapnilsinghrathore9846]

Sir,मेने पहले भी महान आदरणीय श्री रामानुजन जी की paradox के बारे में देखा और समझा था,परंतु आपने बड़े ही सरल तरीके से इसको समझाया और रामानुजन जी के बारे में बताया इसके लिऐ आपका बहुत बहुत आभार 🙏🏻🙏🏻🙂🙂

[@rohitkachare3498]

Mai ek Arts ka student hu. History padh raha tha. S. Ramanujan ji ke bare me padha to shock ho gaya. Etne mahan Ganitdnya the. Salute for his invention in maths..

[@goldandsilver415]

A Mathematitians who breaks the law of Mathematics 😵 Salute to the legend Proud to be an indian

[@ara7i]

Laws of mathematics are never break they are generlize

[@O-Kyklop]

He didn't brake any law. he just didn't know what the Infinite really is.

[@BorutoOtsutsuki__]

​@@O-Kyklopfr there are many loopholes in the term infinite itself , smart mathematicians can make more equations like this

[@O-Kyklop]

@@BorutoOtsutsuki__ The loopholes are in the mind of the ignorant. Basically, the Infinite has no numbers. So, there are not much equations a mathematician can make and this for a simple reason: the equations may have no end but have always a beginning whereas the Infinite has none. Basic school stuff.

[@dhrubaganguly7758]

Why are you breaking english grammar rules?​@@O-Kyklop

[@macbcheesy]

I swear, one of my favorite things about math is that we don't need to speak the same language to understand it. He's taught me more in this video than I learned watching the others.

[@badriiyengar]

But, certainly that is not the evidence to prove here your teacher ( author of the Upload ) is correct here. Everybody knows that 1 = 2 would be cirrect when 0 can be accepted to be denominator as well as Numerator!

[@morbius9537]

@@badriiyengar what crack you smokin?

[@xyyzxg]

​@@badriiyengar I think you skipped simple math. You can't divide a number by a number which doesn't exist that is 0. If divided by 0+ then it tends to infinity.

[@badriiyengar]

@@xyyzxg I have not come here to enter into a debate. My post implied that Zero can not operate as a Denominator, for it would lead to ubsurdity, like producing a number from nothing. Sad part is that you have not understood what I meant( implied). By the way "X" to the power of Zero is 1 only when "X" is any thing but Zero.

[@zebt7477]

Tu galat Sikh rha hai

[@subramaniams6091]

Humble Pranams to Ramanujan Sir. Besides, the tutor’s narration is exceptionally brilliant.🎉

[@OmPrakash-nw4ip]

Proud to be an Indian. Huge respect for S. Ramanujan 🙏🙏🙏🙏

[@gaurangagarwal6508]

Just 1 word Salute to Mr. Ramanujan ji

[@pulsar2977]

that's 5 words...

[@Yashchoudhari00]

@@pulsar2977 lmao bro .but Ramanujan sir 🙏.

[@DakshJee-xx7bj]

Thats 5 words

[@animeshkumar8396]

I feel very proud of a teacher like u who remembers the contribution of legends and make us aware of their story..A BIG SALUTE TO U SIR...And ur way of teaching is just intresting and ADDICTIVE..THANKS for sharing their stories

[@MrDrgdf]

भगवान कसम इससे चूतिया intro आज तक नही देखा

[@Rhythmraj009]

ye sirf paper par proof ho sakta h na ki physically agar hum dhyan se dekhe to numbers ke sath ki bhi khel sakta h par ramanujan was great.......... par hume ye nahi bhulna chaiye ki agar ye equation humne use ki to hum physics ke rules ko tod rahe honge

[@UdaySingh-pp6ee]

Tum chutiye ho..math smjh m aata to tumhe pta chalta ki kya shi hai kya glat... Aise hi upar upar s log kisi pdf s koi problem solve krk tumhe dikhayega aur tumhe lgta h ki bhut shi ..wah wah.. Bhai..ku6 Janna hai to jakr books pdhi..aur smjho.. Tum jaise logo ki wjh s koi bhi teacher bn jata h.. koi bhi Paisa kama rha h.. Aise hi science experiments krne wale channel hai jin salo ko ku6 pta nhi hai kya hota hai reaction m..kyu ho rha h..bs idhr udhr ki copy krk experiment kr denge aur tumhare jaise chutiyo ki line hai hi unko subscribe krne k liye,,

[@madhabimandal2280]

@@Rhythmraj009 bro no,this series is used to prove string theory.Aye phy banate hain,thodta nahi hai.

[@madhabimandal2280]

@@Rhythmraj009 if you don't believe me you can read online materials

[@blacklegend2438]

0 was found by aryabhatta who was Indian and infinity was found by ramanujan sir the first number and last number both were found in india

[@abhishankpaul]

Except for the last one. Infinity was known more or less to all mathematicians across all civilizations. Any sane person will say that numbers have no end

[@subhashpatil2833]

Salute to Ramanujam. Sir you explained in excellent manner. You are real maths master.🙏🙏

[@amaanalrashid8273]

The best channel to fall in love for mathematics

[@silverfangg45]

The proof is wrong

[@amaanalrashid8273]

@@silverfangg45in which class are u studying now

[@silverfangg45]

@@amaanalrashid8273 12 see this kzbin.info/www/bejne/j6asep2Cp5upi6M Ye mathlogger ka video jisne numberphile bolke ek channel usme ek bande ne same proof kia tha ye sir jaisa usko galat bataya hai prove itna simple nahi hai Numberphile video 👉 kzbin.info/www/bejne/rV6sZ4uKi7-Lrdk Ye sir jee ke lia sahi hai lekin general higher topics ke lia nahi pata .

[@konceptmathematics]

Maine Ramanujan summation par atleast isse better video banaya hai

[@konceptmathematics]

And please do subscribe the channel

[@justmath331]

Finally someone made me understand this series without calculus Thank you very much sir

[@ankurgupta9106]

This video is wrong in so many levels. He is fooling you

[@anubhabmondal5342]

It is not the real proof...this proof is proposed by numberphile youtube channel then everyone copied it....this proof does not exist because of divergent series...the actual proof is coming from complex field...

[@ankurgupta9106]

@@anubhabmondal5342 yeah mathaloger made a 40 minutes long video explaining why this proof was wrong.

[@gauranshkapur8977]

@@ankurgupta9106 yes that video explains everything very clearly

[@shashwatINDIAN]

Basic mathematical operations (+-÷×) can only be applied to convergent series. But 1+2+3+4+6+......... is a Divergent series, so mistake starts from the point we assume the value of this series to be a constant just by doing addition substracting. By the way Mathematically applying the basic operations, even 1=2 can be proved and according to that any two given distinct numbers can be proved equal to each other but that's not true. 1≠2, 2≠3, 3≠4,..... But very easily it can be proved that 1=2, 2=3, 3=4,.....

[@sbssarma3517]

Ramanujan is not a mere hero. He is a Mega Star of Mathematics who radiated super brilliantly such that his contemporaries were blindendened by his scintillating lustre of wisdom.

[@O-Kyklop]

Ramanujan didn't understand the concept of Infinity and made gross mistakes because of that, as the so called Paradox in this video. And the guy in this video, "explaining" the Paradox seems not to understand much better the question of Infinity.

[@someone-jl4sj]

​@@O-KyklopRamanujan was correct it is the video that is wrong

[@O-Kyklop]

@@someone-jl4sj No fellow, he wasn't. There is no way Infinity being -1/12. First off, because these sums he uses to demonstrate it are not Infinite. There are some more reasons but this one is sufficient to refute it.

[@someone-jl4sj]

@@O-Kyklop Ramanujan never said that -1/12 represents this sum. What Ramanujan showed was that this was analytical continuation of Riemann Zeta function. And this is the value of Zeta(-1). For more information search Riemann Zeta function.

[@O-Kyklop]

@@someone-jl4sj It xdoesn't change anything. If the result is oo=-1/12, is wrong.

[@paurusshukl4892]

Rules of finite maths don't apply to infinite series.

[@gss-motivation4903]

True.

[@sidindian1982]

While preparing for data science mathematics ( linear algebra CALCULUS, STATS & discrete mathematics )..i truly think of Sri Ramanujan sir 🙏❤️❤️🙏🇮🇳

[@samiullahk7223]

Y not god?

[@aadityagururani7519]

​@@samiullahk7223 why not ramanujan?

[@cxnaruto4931]

Maths God= ramanujan hence proved

[@cxnaruto4931]

@@IsaacNewton818 sir pliz laws vapas lelo apne 🙏

[@gautamgupta6029]

THIS VIDEO IS WORTH #1 TRENDING!! 👍👍👍 JUST AMAZING SIR !! SALUTE TO AMAN SIR .. AND COUNTRY'S PROUD SRI.RAMANUJAN SIR 🙏🙏

[@silverfangg45]

The proof is wrong bro

[@Rahul.G.Paikaray27]

Sahi bate de

[@silverfangg45]

@@Rahul.G.Paikaray27 First of all the prove is wrong A and B are divergent series . And its copied from numberphile video kzbin.info/www/bejne/rV6sZ4uKi7-Lrdk which is itself wrong which was rectified by mathlogger video 👉 kzbin.info/www/bejne/j6asep2Cp5upi6M The actual proof is not so simple he is proofing like 1=2

[@Rahul.G.Paikaray27]

@@silverfangg45 thanks brother

[@binodtharu8348]

@@silverfangg45 i agree that this proof is wrong because its divergent series but this proof is not like proof of 1=2, in that proof we use the thing that (2-1)^2=(1-2)^2 type things......

[@APSAHAYMP]

Rearrangement and distributive law is not allowed in infinite series...only in absolutely convergent series it can be done...... Even the proof using riemann zeta function would be wrong because -1 is not in the domain of zeta function. Before teaching for jee it is absolutely essential to do graduation in the subject.....so that such videos do not end abruptly without any disclaimer.

[@deshbhktA]

Genius Ramanujan ji 🙏 Thanks Aman ji for presenting it nicely, and praising the hero of Maths from India. 🇮🇳✌️

[@saranathantg]

While my great admiration is for Ramanujan, I am grateful to you for bringing to light in simple way his greatness. Thank you Sir

[@tango1980Mwj]

sadly we live ina country where people like Salman, SRK, Dhoni, Kohli..... (infinite series)... get more importance then people like Ramanujan... I live 4 kms from Ramanujans house in chennai... Love u bhai from chennai..

[@ankhi6604]

Why are you even mentioning them? They are expert in their fields. I know that Ramanujun doesn't get that much importance but you can compliment him without mocking others who are genius in their profession.

[@akshitrawat82]

@@ankhi6604 yess! Every body is perfect in their own field.. I pay huge Respect towards Ramanujan sir 😄😃

[@ferdousbhuiya]

I could not hold my tears. How it is possible. Real hero of Math. Salute you Boss.

[@sopusuryawanshi6934]

Wrong hai bhai paradox

[@yourenglishtour]

Ramanujan's story is mind blowing. Eyes tear when I hear about his magical mind of maths...😍

[@chaitanyatale4666]

SALUTE TO THE GREATEST MATHEMATICIAN OF ALL TIMES RAMANUJAN SIR🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻

[@jitendramohan7500]

B series can be grouped as (1-2)+(3-4)+++ and sum tends to - infinity so it is divergent series so sub or add of series B to other series as divergent with convergent leads to indeterminate form results in paradix

[@tanmaynayak2250]

Bhai kya keh raha samaj ma nahi aa raha

[@Siddharth_Mauryaa]

@@tanmaynayak2250 BSC kro tb smj me ayega

[@Mr.Ak.2608]

Its divergent series, so can't be converge to any real no. 😂😂 Maths hons karo tab samjh ayega

[@soumyajitsarkar507]

​@@Mr.Ak.2608 the actual proof is by remmans zeta function

[@Mr.Ak.2608]

@@soumyajitsarkar507 by both reimann zeta and direchlet eta functions

[@bibeksubedi2909]

My reaction was Oh My God after he proved it😂😂❤ Hats off to Ramanajun and Aman sir🙏

[@saquibmohammad2860]

For the sake of students, the series 1+2+3+.... does not REALLY equate to -1/12. What's actually happening is actually a consequence of a result called Riemann Rearrangement Theorem. The theorem states (very loosely I'm not going in to detail) that if the order of terms in a particular series are shuffled, or rearranged, an infinite series can be used to give any number of any choice. For example, let us take 1-1+1-1+..... Now if I want to rearrange this sequence, I can choose to write it like this. 1+1-1+ 1+1-1+.... Since both positive 1's and -1's are infinite, I can write this indefinitely but by earlier logic as presented in the video, the sum is tending towards 2/3. Now which one is correct? The answer is both. Depending on how you write the series, the sum changes. So in a way, the answer depends on the way the series is written. So, if you see this equation again, understand that this answer comes out to be -1/12 only when this series is written in this particular fashion. And it can be made to be anything. If we write it in some other way.

[@bhausahebkunjir]

The series is Divergent . You cannot perform these oerations. Here a mistake is being glorified for publicity. If done for fun, the should have been clrified.

[@saquibmohammad2860]

@@bhausahebkunjir it's Divergent but not absolutely Divergent. That's why I said the sum is not really equal to -1/12 when written as a sum of natural numbers. That's Riemann's rearrangement theorem, essentially stating that series that are Divergent but not absolutely can be rearranged to give any sum.

[@prabhassen7287]

This is about popular mathematics and about a genius who did not have any formal mathematical training. I think it is unfair to bring in modern day mathematical rigors into it. Hardy understood this and took this unassuming genius under his wings and presented him to the modern world of mathematical rigors d further research. We can only wonder how his intuitive thoughts are now used in modern Era mathematics and physics.

[@harshbhushanpathak2392]

You are really doing a good work and this needs to be continue sir. The moment you found the value of A I was shocked this is really the magic of maths . Salute to the legend S. Ramanujan 🙏🙏

[@ankurgupta9106]

This video is wrong

[@AdityaRaj-yu2ir]

@@ankurgupta9106 Yess

[@yagami1130]

This video is 100 percent wrong, since distribution law isn't correct in infinite series

[@harshbhushanpathak2392]

@Ankur Gupta @Aditya Raj @yagami this is a paradox which actually is used for calculation of electric forces between two uncharged plate in vacuum , and also in string theory in real time. So it is definitely correct .

[@yagami1130]

@@harshbhushanpathak2392 yes its indeed true but the way its proved in this video is totally wrong, he must prove it using zeta function...that's what Ramanuja did.

[@KedarAhire411007]

This is the great way of giving tribute to Ramanujan ji...Thank you Aman sir...🙏👏

[@zarapkarajinkya4034]

I think the paradox happened because series A was supposed to be 0 but became 1/2

[@praveenkumarsingh1436]

Not always zero. It depends on the number of terms in the series, whether it is odd or even if it is even sum is 0 if odd, sum is 1.

[@shivamkumarrai8598]

​@@praveenkumarsingh1436but in no situation it can be 1/2

[@nitinmaharana3706]

@@shivamkumarrai8598 They used average because we really cant if the last digit of infinity is odd or even ,so we are forced to take 1/2 but its not accurate we say it as the closest sum of all natural numbers.

[@abhishankpaul]

You don't know whether infinity is odd or even. If you consider the partial sums, if the series contains even terms, sum is 0 else 1. There is no way you can have 1/2. You cannot take averages as well

[@Aakashmahto17]

Next shri Ramanujan of Indian Aman sir 💓

[@krushnachandrarath3652]

Thanks for the post. May I add that this paradox is used in string theory. Casimir's effect in physics on existence of attraction between two charged particles in vacuum is explained by him using this paradox.

[@soumiksaha8484]

Thanks for fyi

[@zebt7477]

We use a made up value to prove a made up theory doesn't mean your made up value is true

[@alien3200]

This prove is wrong. I can prove it to be -1/8. Bhai its a divergent series and divergent series ka sum infinite hota hai. Kisi finite value pe converge nai hota. Its Like using infinite GP wala formula when the common ratio is more than 1

[@ayyasuddin3394]

The Man Who Knew Infinity (Srinivasa Ramanujan)🙏🏻🙏🏻🙏🏻

[@KSJGaming]

imagine a number n such that 1+2+3+...+n=-1/12 we get n and then u see 1+2+3+...+infinity=-1/12 dont u think infinity will be defined then?

[@shiveshkumar3694]

For their sum be -1/12 n must be infinity which we cannot imagine

[@lohitadityanaik8144]

India is blessed with legends like Ramanujan sir

[@ritasagar77]

hamare desh ko AAP jese teacher ki jarurat hai jo hume en mahan vidyano se rubaru karaye pata nahi aaj kal ke sabhi log en mahan logo ki baat hi nahi karte

[@jsk5549]

@@AnmolSah27 Tere bap se jayada Knowledge hai sir ka

[@Ankitkumar-fi4rc]

@@AnmolSah27 Tera Pura family sale inka mukbla nahi kar sakta h , aur tu to abhi bachcha h 🤣🤣🤣

[@Ankitkumar-fi4rc]

@@jsk5549 ha bro uska baap ka baaap ka baap ka baap ......... Infinite time tak koi utna nahi janta jitna aman sir ,🤣🤣🤣

[@ankurgupta9106]

The proof presented in the video is completely wrong

[@Ankitkumar-fi4rc]

@@ankurgupta9106 are yaar dekho thik se

[@himeshmaan8766]

Sir said fatt gyi thi logo ki 😂😂😂😂. . Aankhen 😅

[@methleshkoshle7643]

What a gift to the world Ramanujan sir. You are great teacher sir 👍.

[@aadityasharma5948]

The man who knew infinity ♾️♾️♾️

[@Crackdsssbtgt]

I started to like each and every videos of yours... Your way of explanation is incredible... I also want to be a teacher like you are!

[@AdityaKumar-ji8dk]

Ramanujan proved his theorems when he was dying...those were the last 2-3 years of his life when he prepared all the proves of his theorems...he worked in very poor health conditions...blood coming out of his mouth with cough, but still writing...you can see such scenes in the movie 'the man who knew infinity'. He devoted his whole life to to bring out his theorems and formulae so that all the theorems will be preserved. He worked for giving the world something great, not for his own wants. He is a true legend...a mathematician which will be remembered forever.

[@shivamthakkar6706]

Thank you Ramanujan sir for your great contribution in mathematics. I wish I could meet you.🇮🇳🙂

[@HRajMNNIT]

The explanation just blown my mind 🤯🤯🤯🤯

[@ankur20010]

This problem is covered in the first basic real analysis course. And there are a lot more such examples in the real analysis book by terry tao The reason for this paradox is that you can't do operations as mentioned in the video , on an infinite series. You need to prove the convergence first and then justify the regrouping etc.

[@yashrajchouhan82]

Bro, sir Ramanujan was much more beyond than our thinking, he would have thought about that before

[@AdityaRaj-yu2ir]

@@yashrajchouhan82 Bhai tune kitni maths padhi hai. Ramanujan was a genius but not a god he can be wrong.

[@todten1476]

@@AdityaRaj-yu2ir he could be wrong but then again all his equation were proof later years. And his given equation is used till today to study blackholes. Remember black hole was first predicted in 1916 and ramanunjan died around 1920. Now imagine if he lived more than 32 years. Without any good education background he reached G.H Hardy with his math

[@yashrajchouhan82]

@@AdityaRaj-yu2ir Bhai Ramanujan ke time par ya uske baad bhi kayi mathematicians the par kabhi yeh suna ki kisine unhe wrong proof kiya ho, humne toh yeh hi suna ki jo koi naa kar paya woh Ramanujan sir ne kiya toh I think he's the mathematician God and yadi yeh baat galat hoti toh mathematicians bohot pehle hi proof kar chuke hote kyuki duniya mein tere jaise bohot log hain jo Indians ki success se jalte hain aur hn paradox ka matlab hi yeh hota hai ki dekhne par galat lage par vastavikta mein sahi ho

[@AdityaRaj-yu2ir]

@@yashrajchouhan82 tumhari knowledge kam hai

[@CD10ANIL]

The key of infinity in math (Still not known rule) , like of BODMASS rule, is that nothing can be removed from infinity once it added to it, though can be rearranged and add more but can not remove, this is what is missing above and causes such paradox. Sometimes simplicity avoids big mistake. This is like a black hole , one is talking about taking back something from blackhole. So the statement that the sum of the infinite series 1+2+3+...infinity is equal to -1/12 this result is based on the assumption that division by zero is allowed. but division by zero is undefined, so the sum of the series is also undefined. There is a mathematical theorem that states that the sum of an infinite geometric series is equal to a / (1-r), where a is the first term of the series and r is the common ratio between the terms of the series. In the case of the series 1+2+3+...infinity, the first term is a=1 and the common ratio is r=1. So, the sum of the series would be: S = 1 / (1-1) = 1 / 0 However, as I mentioned before, division by zero is undefined. So, the sum of the series is also undefined.

[@yashsingh.113]

I think this person is the definition of teacher for me because once when I was a child my grandfather told me about Ramanujan paradox and I was very confused as to how it is possible, and finally my doubts were cleared and I learned new thinking in mathematics Thank you so much sir

[@nirajkhare3915]

Also you cannot rearrange terms in an infinite series without changing the sum (if it's defined) unless it converges absolutely. Please teach convergence first and then see the work of Ramanujan using extension of complex analytical function by

[@biplabmahato119]

Yes, with out absolutely convergent we cannot rearrange the terms. This prove is wrong.

[@Ramu-bw4ub]

Without Taylor series expansion?? I think Taylor series should be best applicable here.

[@princeladdha65]

A huge salute to ramanujan , such a great mathamatician who born in india 🙏🙏 Proud to be an indian🇮🇳❤

[@rrawatsachin93]

Jab jab me The great mathematician Ramanujan ke baare me sunta sach me etana proud hota ki aankho me aashu aa jaate hai, proud to be an indian. Jai hind

[@-SARTHAKSHARMA]

Ramanujan sir was uncontrolled nuclear rxn salute to such personality in just of 32 age 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥

[@adarshiitguwahati8101]

X=2+4+8+16+32....... X=2+2(2+4+8+16.....) X=2+2X X=-2 I have prooved one paradox 🤣🤣

[@utkarshiitbhu4204]

Bro diverging series hai 🤦🤦 Memes kum dekha kro

[@baldricosta972]

Abe tu diverging series men nahi laga sakta sir ne 1-1+1-1+1 par lagaya hai wo diverging nahi hai

[@adarshiitguwahati8101]

@@utkarshiitbhu4204 ha bhai pta hai mai mazak kr rha tha mige bhi pta h ki ue diverging me nhi lagta

[@utkarshiitbhu4204]

@@adarshiitguwahati8101 first reply zyada serious hogya lol

[@adarshiitguwahati8101]

@@utkarshiitbhu4204 haa

[@kamleshdevi-fg2br]

Sir, Please make a video on NIKOLA TESLA SIR🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🇮🇳

[@silverfangg45]

@Abhay Pandey naam batana to Zara indian scientist Google search mat karna

[@kamleshdevi-fg2br]

@Abhay Pandey Bhai, INDIAN SCIENTISTS भी महान थे पर ,NIKOLA TESLA ki kahani सुन लेना sir से एक बार ,आप चोक जाओगे 🙏🏻

[@harshjais369]

@@kamleshdevi-fg2br @kamlesh devi Yes Tesla was a genius. He's father of our today's modern world. He always thinks for mankind. We humans should credit all the great persons for their work instead of arguing who is indian or ..., who is great than ..., etc.

[@abhishekbhuyan3576]

@@silverfangg45 abe Bengali tu apni aaurate bechne me focus kar. india pe already kai saare mathematicians, philosophers or academics hai.

[@MJ_Rocks354]

GREAT mathematician mr ramanujan sir

[@AkshitGoyal-ki]

he was lucky to have such a brain , every 1in a billion person is BORN WITH SPECIAL BRAIN , he did'nt do anything to achieve that brain , it was served to him in a silver plate as soon as he took birth,' i know this sounds like a hate comment , but it is the truth , i rather respect those ppl who work hard and achieve that lvl of mind instead of just being lucky and getting it by birth

[@SakibKhan-xc1nn]

Unbelievable result Ramanujan sir is greatest person ever❤❤❤❤❤

[@surajv1986]

Thanks a lot Sir for taking the efforts to explain lucidly the works of our great Mathematician Shri Ramanujan!!!

[@satveersingh2664]

Although I m not from Mathematics ,I can understand u' r teaching ,u r best teacher in Maths .

[@user-bunny_01]

We can also prove A = ½ ..in this method :- 1-1+1-1+1-1+1..... Its like infinite G.P whose common ratio is -1 and first term is 1 " sum of infinite G.P = first term / 1-common ratio " => 1/1-(-1) = 1/2

[@satoru_gojo_720]

3:06 🫡🫡🫡🫡🫡🫡🫡🫡🫡🫡🫡🫡🫡

[@krishnkantshridhar664]

Sir I am very curious and wants to study about more such equations by you please start a Ramanujan Series where you teach us these type equations .Its my humble request .🙏🙏🙏🙏

[@Yuvrajsingh-3ub]

Greatest mathematician... Ever on the earth. 🌎🌎

[@productionmillionviewsz5338]

Great ji and He always said that Mata is telling me maths and he is great

[@HoshangGovil]

By ChatGPT: The Ramanujan Paradox is a mathematical result that appears to contradict common sense, as well as some basic principles of calculus. It is named after the Indian mathematician Srinivasa Ramanujan, who discovered the paradox in the early 20th century. The paradox involves a sum of an infinite series, similar to the divergent series mentioned in the previous question. Specifically, the paradoxical result arises from considering the sum of all positive integers and the sum of their squares: 1 + 2 + 3 + 4 + ... = -1/12 1^2 + 2^2 + 3^2 + 4^2 + ... = 0 These results may seem surprising or counterintuitive, as it appears that we are summing an infinite number of positive terms to obtain a negative value in the first equation. However, it is important to note that these results do not represent actual sums in the usual sense. Instead, they are examples of a more general concept in mathematics called analytic continuation, which involves extending a function beyond its original domain in a way that preserves certain properties. The Ramanujan Paradox has been a topic of much debate and controversy over the years, with some arguing that the paradoxical results are simply mathematical artifacts with no physical significance, while others suggest that they may have applications in areas such as quantum field theory and string theory.

[@curiosityandlearningforciv662]

Hello Mr. Aman, Captain XYZ( Indian armed forces) this side, I donot have a formal background of maths but I gave a thought on this series and found out following assumption flow in your calculations : You assumed 1+2+3+4........= S Now by assuming the series sum to be a finite variable S, you have forced the certainty on infinity(because only after that you were able to solve B =-4S +S =-3S but actually what you are solving is - -4* infinity + infinity). And due to this we see such an absurd answer!!

[@animasharma2650]

Shut up until u know infinity

[@sarfaraz660661]

A blind person perceive all hole is same.

[@bjhonusa]

Term Infinity means some number you can not imagine. It does not means it's beyond calculation. Read the maths carefully.

[@dhruvchaudhary4684]

​@@animasharma2650😂 ok wait

[@aadilansari5997]

Sir you have the mind to question and query. Please read up quora especially Alon Amit.. You are right, when dignify infinity with the title of a number, you are inadvertently playing fast and loose with the concept of a number. For example in a normal number system if a+b = a+ c then b=c. But if you add infinity to the normal number set then Inf + b = Inf+c doe not allow us to infer that b= c.

[@nihal7771]

😶kamse kam 5-6 mahino se dimag kharab ho gaya tha yeh jaan ke ki sum of natural number till infinity -1/12 hota hai but aaj finally proof mil gaya tho accha lag raha hai Thanks for this video sir ji

[@sauravsutar2125]

Bhai iska proof toh 2014 se youtube channel PE hai... Nd still it is a illogical proof

[@vishalyadav0099]

India is blessed with legends like Ramanujan Sir.. ..

[@subhashchandraparida4320]

Really he was a Indian geñius. Really, he is Mother's gift to not only India but to the World.

[@nishantverma2966]

It's pure imagination and can't be thought by ordinary mind Ramanujan Sir was inhuman

[@techmaster6587]

The Man Who Knew Infinity *JAI NAMAGIRI DEVI* 🙏🙏

[@ashwanibeohar8172]

As such in the series where the terms are alternate +ve and -ve, the sum depends on the thing that Whether last term is +ve or -ve. The sum will be +ve if last term is +ve, and sum is -ve if last digit is -ve. As such such serieses have two different sum for n=+ve, and n=-ve That is A1 and A2 In ramanujam paradox A1 and A2 are taken as equal , which leads to incorrect results.

[@RS_Official07]

7:32 the first step is itself wrong because if a series is going upto infinity then how can you take something equal to infinity when it's value is not defined Also if u are just naming the series with A how did u take the series EQUAL to A. Similar case with S and B series as well. Hope you understand

[@parteek_bhamania]

Apne physics wallah kuchh kisi karn se hi chhoda hoga ya jo time alakh sir ka tha wo aap ko soot nahi kar raha hoga. Lekin sir ek baat bataun apse badhiya maths teacher maine aaj tak nahi dekha aur sayad na hi age kabhi dekhoon ga. Logo ka kya hai wo to ease hi hate felate hain but sir jab main bada hokar kuchh ban jaunga na to alakh sir se to kya hi pata lekin apse jaroor milonga. Thanks sir for giving me this type of mathematics knowledge jab main apse maths padhta hoon to sach batun maza hi aa jata hai. Once more thank so much 😊😊🙏🙏

[@NageshwarRTMehta]

Sum of series of number greater than 1 is always ♾️infinite As it is solved in all steps if you think about relative elements taken from different series have so much gappings....... A And if you think answer this series is right then I have an idea that you can give me that amount of money and there is no loss of you 😄 But salute to RAMANUJAN sir 🇮🇳🇮🇳 May be people are unable to find wrong step involved in this solution.... 😇

[@soujanyoghosh9174]

♾️-♾️ is indeterminate form

[@dafureveerbhadra2772]

Bro, this result helps in solving string thoery. No other value of sum of natural numbers solve string theory

[@dafureveerbhadra2772]

Also this proof is not actual, the actual one is given by using gamma function

[@shibanjanmukherjee3706]

Yes this proof is wrong,actual proof requires gamma function and complex analysis

[@yashrajchouhan82]

What!!! You people are saying that Ramanujan has done wrong

[@rfsplayer162]

-1/12= reciprocal - 12 divide by -1 = -12=-12/1=-12 multiply 1 = -12+0=-12=-12 divided by 0=0 Hence infinity =0 Amaan

[@p.h.gaming9319]

Perfect

[@ramjoshi9278]

thats my point no one is comparable to sri srinivasa ramanujan sir a great mathematician a great follower of maa

[@rajeshmalviya1968]

Thank you brother.....I am maths lover....and while watching this clip, many times my eyes got wet in love with The Great and genius Poojya Ramanujan Sir........your way of explanation is beautiful........❤❤❤❤❤🙏🙏🙏🙏🙏

[@AvnishKumar-bt1pd]

Series A is discussed by Mohit Tyagi in maths for fun

[@mantoshmandal3999]

Ramanujan sir jaisa na koi tha aur na koi honge mera dawa hai.. ❤❤❤🎉🎉🎉

[@bharatvarsha7]

this paradox happens because we dont know to use infinity yet..we cant subtract infinity to infinity, it wont give you zero or any positive or negative number..here in this equation this paradox happened because it took infinity substracted from infinity as ZERO which is actually not zero..but Ramanujam used this paradox to solve some divergent series..the paradox is neither true or false but just what its defined, and used for infinite series to solve equations

[@Arv.-]

Excellent!

[@Sumit_memer.]

RAMANUJAN JI MAHARAJ KI JAI PURE DUNIYA ME JAIJAIKAR HO AAP MAHAN HA (RAMANUJAN JI AAP MAHAN HO)

[@sudiptasamajdar9156]

{n} is a divergent sequence, so sum of all natural number canot be a finite quantity. {(-1) ^n+1. n} is also not convergent it is undefined oscillation. So we can't assume any real quantity A or B as a sum of this series.

[@soumyaghosh8823]

Only Absolutely convergent series can make rearrangement and sum remains unaltered by Riemanns theorem

[@rudradansena6298]

Yes that's true but who will teach this kind of bhakt where real analysis not exist for this kind of teachers , and I think ramanujan had no idea about the convergence so that he has did such type of blunder .

[@jotawski]

ฟังไม่รู้เรื่อง แต่เข้าใจครับ ขอบคุณมากนัก นับถือ 🙏🙏🙏 ❤️❤️❤️

[@jotawski]

@Som Verma Yes, I am Thai.

[@XYP-ER_GAMING]

Bhai Comment me saare bade bade mathematician bethe hai or me biology ka student galti se yaha aa gya💀💀💀

[@milindjathar7438]

Can this theory be used in cancer treatment. Uncontrolled growth of sales. Still human dies means equal value= -1/12.

[@Amit1994-g9i]

These things work only if the series converge, else there exists a countability of infinity which states that every infinity is not equal.

[@ayushsinha1298]

Yep I'm a jee aspirant and was thinking the same that when he replaced and take common minus and say it A ,I myself thought that how "that" infinity in which +1 was included and how "that" infinity in which 1 was not included can be same????

[@rohanmishra23]

@@ayushsinha1298 because if we add 1 in infinity it is also an infinity

[@lalitchoudhary3540]

Exactly, what I want to say

[@theseeker9591]

I understand what u say but do u have a reason to say that algebra don't work if series is divergent.

[@ashishj2358]

kzbin.info/www/bejne/j6asep2Cp5upi6M

[@deltechdiaries5907]

the greatest mathematician ever

[@joydebnath2111]

Sir you are great. I tried it in finite case 🙂 B=1-2+3-4+5-6+.........n=-1-1-1-1-........n/2=-n/2 S=1+2+3+4+........n Now, S+B=2(1+3+5+.......n/2)=2×n^2/4=n^2/2 Or,S=n^2/2-B=n^2/2+n/2=n(n+1)/2 And S-B=2(2+4+6+........n/2)=2×n/2×(n/2+1)=n(n+2)/2 Or,S=n(n+2)/2+B=n(n+2)/2-n/2=n(n+1)/2 In both case sum of n natural number is n(n+1)/2 which is true.🙏

[@sahilthakur2769]

I just schocked at this and started making notes . Meanwhile I never studied calculus with this much interest ❤️❤️.

[@ajslive334]

Sum of all natural numbers is -1/12 Which is impossible but the way he proved is amazing But it also shows that if we take another series of a and b of a different type then a different answer would also come But the truth is that sum of all natural numbers will never be negative and cannot be solved by anyone in the universe

[@inquisitiveindian36]

Yes. That's what paradox is defined as.

[@GursewakSinghOfficial]

GAJAB SIRJI 🔥🔥🔥🔥 WE WANT MORE VIDEOS LIKE THIS ❤

[@dhruvpathak3180]

Salute to Sir S.Ramanujan

[@yashkumarharit5930]

He was the man who knew infinity ,🙌🙌🙌🔥🔥🔥

[@1543_T]

salute to the one who got behind the properties like closure! 💯🔥⚡💯

[@utuberaj60]

One more point Sir. Can we not also prove the sum of infinite natural nos in an Arithmetic series to be infinity using the basic formula S= n(n+1)/2, and ser n= infinity?

[@siddharthreddy9461]

​​@itzaadi4627o it isn't Infact, the above sum is tending or diverging to infinity under regular mathematical axioms for finite real numbers

[@anandnarayan3970]

There is one error in the proof where you had taken the value of A as 1/2 because A is an infinite G.P. and in the infinite GP sum formula if you put the value of first term of A i.e.1 and common ratio of A i.e. --1, you will get sum =1/2 but it is not correct because infinite GP sum formula can only be used when mod of common ratio is greater than 0 and less than 1 but here mod of common ratio is 1, hence we cannot use the infinite GP sum formula,hence 1/2 cannot be the answer of this particular GP . Therefore A is not equal to 1/2 We can only say that A can be 0 when there are even terms in the series and A is 1 when there are odd terms in the series( I said this using the formula of sum of n terms in GP) Since the value of A is taken as wrong whole process is wrong . Note---- I am not saying Sir Ramanujan said wrong about the sum of infinite natural numbers , I am just saying this particular process is wrong.

[@satyanarayanpatra7357]

Great salute to our Hero Ramanujan 😎 BTW nice explanation Sir thanks for the video 😊

[@ritxve]

Isme problem isliye aa rhi h kyuki ∞ terms h aur ∞ koi bhi ek specific number nhi h wo khud hi thik se defined nhi For example, let's say X = ∞ Also we know that ∞ + 1 is also ∞ » X + 1 = X » 1= X - X » 1 = 0 (LOL) As it's not true reason is that ∞-∞ is simply inderminate and not zero.

[@MrRaghavann]

Correct yar something is wrong here.