REAL TRUTH Behind Ramanujan Paradox | 1+2+3+4+....... = -1/12 | NMS Sir

[@iitd.priyanshupandey]

Please don't spread what you don't know. When mathematicians say that the sum of all positive integers is \(-1/12\), they are referring to this value in the context of analytic continuation and Ramanujan summation, not in the traditional arithmetic sense. It’s a result that has profound implications in theoretical physics, particularly in string theory and quantum mechanics, where it helps to regularize otherwise divergent series. It is a profound result that bridges the gap between pure mathematics and theoretical physics, showing the power and applicability of advanced mathematical concepts in understanding the universe. In string theory, particularly in bosonic string theory, the concept of the sum \(-1/12\) appears naturally. When calculating the Casimir energy (the vacuum energy) of a string, this sum helps regularize infinities and yields meaningful physical results. **Casimir Effect:** In quantum field theory, the Casimir effect is a physical force arising from a quantized field. The \(-1/12\) value is essential in these calculations to ensure that the energy density between two conducting plates is finite and physically meaningful. In quantum field theory, regularization and renormalization techniques often lead to sums of divergent series. The \(-1/12\) result helps handle these divergences and provide finite results. **Regularization Techniques:** When calculating loop diagrams in QFT, divergent sums appear. Using techniques like zeta function regularization, the divergent sums can be assigned finite values, with \(-1/12\) being a classic example. Just for the sake of getting views, don't mislead students. Peace!!

[@MathsMantrs]

Sierpiński proved that rearranging only the positive terms one can obtain a series converging to any prescribed value less than or equal to the sum of the original series, but larger values in general cannot be attained.so Ramanujan was correct . We can make divergent series to converge any real number by rearrangement Thank you for your valuable comment

[@IllegalBangladeshiImmigrants]

Yes, someone said it. Thank you.

[@SouvikDey-gy7dv]

And also sting theory...

[@IllegalBangladeshiImmigrants]

@@SouvikDey-gy7dv sting?

[@lakshays833]

🤓☝️

[@rudraksh80]

ये हमारा दुर्भाग्य है कि वे महापुरुष हमारे बीच नही हैं जो इस का उत्तर दे श्रीनिवास: रामनुजन

[@justnowi8967]

This question actually has several interpretations. 1. This reference is related to definite integration. You may know the formula of ∑n = n(n+1)/2. If you plot the curve of this function as, y=(x^2+x)/2, you get a parabola, which is open from both left and right extreme. But there's a small bounded region in 3rd quadrant,whose area equals 1/12 units and as convention that it may be written as -1/12. 2. Ramanujan was a genius mathematician and he may have seen something that the current mathematical models were not enough to express those ideas. Also, because of lack of traditional educational, he developed different ways, signs of writing. So some mathematicians say that result is completely true, if you change the meaning of the symbol '='. Its not 'is equal to' its 'is associated with'. And then these equations hold true.

[@gauravsingh283]

Ramanujan summation is based upon Riemann's zeta function anyone making video on it must know about thay

[@eduvlogger4384]

Thanks tcah ptg

[@gauravsingh283]

@DoomsdayProphet- oversmart nhi ye sab views ke liye kiya gya hai

[@shivanshnigam4015]

@@gauravsingh283 uske bina bhi iska proof likha ja sakta hai par ramanujan ne kis methode se kiya tha yeh nahi pata

[@greenvision4387]

Ramanujan greatest mathematician the .Aur aise discussion per wo khush hote....kyonki ye pragati ki nisani hai.

[@NMSPhysicsISAC]

So true. Keep growing

[@gauravsingh283]

Do you even know about euler masheroni constant??

[@malhotraji9563]

​@@gauravsingh283 I don't know correctly may be it is a part of complex numbers

[@gauravsingh283]

@@malhotraji9563 do you know he is wrong and this video is just for views he is completely wrong at 12:32 i can prove using integration inequality

[@shrutisarangi8387]

One of the greatest* Directly greatest khke baki mathematicians ki disrespect kr rhe ho

[@gauravsingh283]

Sir by all respect you are wrong at 12:32 because every series whose last term is very small doesn't means that it will converge for example the harmonic sum decrease at every step still its divergent proved using integral test

[@PrajwalV1729]

Yaa bro 🎉🎉

[@ramharshdandekar5048]

You are correct 👍 This series is convergent lebnitz test for alternating series😊

[@svgstark3742]

This comment should be on top

[@ExtraDark093]

True 🫡

[@gauravsingh283]

@@svgstark3742 thanks bhai

[@mallikarjunpatil5475]

Sir, Ramanujan was still not wrong. You are right that this is not possible in case of normal addition and standard calculus. But Ramanujan defined these sums in different mathematical context. Normal addition doesn't work for divergent series. Ramanujan invented a new way of summing, now called "Ramanujan summation" ( en.wikipedia.org/wiki/Ramanujan_summation ) to assign a value to divergent infinite series in a way that has interesting mathematical properties. In fact, this has some applications in quantum field theory and string theory for getting rid of infinities.

[@LakshyaVN]

Cool

[@laveshsinghrajput8520]

Wow

[@jatinyadav178]

Good to Go. 😊 Ramanujan had his own theories related to zeros.

[@parallelverse8593]

Ramanujan is not wrong in actual , because the summation he proposed is exactly true according to maths and is significant in higher dimensional Mathematics and physics ✔️ and many mathematicians later also found the same summation by different methods for example when you use ' Riemann Zetta function' to find sum of these sequence we actually get these results which Ramanujan Proposed and his summation is regarded as true as per Mathematics and also these summation are used in Quantum Physics . So although these sums are non intuitive but actually true when we deal with "Higher dimensional mathematics " 👍🏻✔️ .

[@Mortals_o]

Please tell the application of higher dimensional mathematics !

[@hiden6202]

There are even some ways by which you get different ans.

[@See_me_iF_U_can]

​@@Mortals_o 😂

[@galaxyvlogs4.8m16]

​@@Mortals_o😂

[@parallelverse8593]

@@Mortals_o So Higher Dimensional mathematics is basically theorems , results and research in mathematics useful to study the dimensions beyond three physical dimensions , These are used in understanding the fundamental structure of our universe , like in Quantum Field theory and String theory .

[@Story_of_science_]

The idea was put forward by reimann using something called zeta function and analytical continuation . -1/12 is value of zeta function at input of -1 but zeta function has domain of (1,infinity) But if we use analytic continuation, we get -1/12

[@kk-vx5ty]

A Bro are you a student?

[@Story_of_science_]

@@kk-vx5ty nope. I m a teacher as well

[@Tanvir2025]

​@@Story_of_science_ then is it correct?

[@MathsMantrs]

Think about Riemann rearrangement theorem sir , he was not wrong. He had used rearrangement of oscilatory series. And if a series is divergent then it can be made to converge any real number

[@pri012]

Inko maths nhi aata, sirf physics aata hai...aur ye aayein hai Ramanujan ko galat bolne

[@natural_science2]

Ramanujan was not the student of competitive exam preparation. These summation are in terms of analytic continuation not in usual arithmetic summation of natural numbers. Its widely used later by eminent theoretical physicist Richard Feynman and others to get rid of infinities and got Noble Prize later for his work in quantum electrodynamics, basically using the convergent integral at some point. Are you kidding that these people were not able to judge infinities. 😅😅😂😂😂 Its so hilarious that you are telling that the Mathematician Ramanujan didn't judge infinity correctly. He was not the coaching centre teacher who read and solved few previous year questions and books, and wrote these equations.

[@SHIVAMNm-rc3zx]

Thanks, For some time I thought how can Ramanujan be wrong, then after reading your comments I realized that this master himself is wrong, Thanks again 😊

[@anupammishra2927]

Ha yrr these teachers think they are higher than the mathematicians who have devoted their lifetime to this specific work🎉

[@ravinder4990]

He was super genius.. Normal people even cant understand the way he did.. It is very far to find the logics behind his calculations..

[@krishnamania1]

Yes sir , mujhe bhi yahi laga tha , mere sare classmates mante hi nhi the or kahte the ki mai unki disrespect kar raha hoon . Also yeh unke kisi research paper mai bhi nhi hai (unki notebook mai hai) , toh shyad yeh kuch unka chota mota mazak hi ho skta hai , tabhi unhone publish nhi kiya ... Agar series divergent hai toh kuch socho hi mat , fir sare proof jo uski value nikalenge vo sirf "false proof" hai. Yes sir basic Real Analysis

[@mishthiexplores3732]

Heroism thrives in not just seclusion and acceptance of the theorem's given by geniuses but in thinking and creating n numbers of questions on those theorems... You're a great symbol of Hero who is is inspiring this generations to think and find our self intuition about th existance ... we respect you more than the then proff. Hardy who couldn't figure out these mistakes........ I'm a physics teacher andgot to say that yes i love u boss...and thank you

[@quantika7007]

Sir I am solving Resnick Halliday. Where to find Solutions???

[@factbuzz7646]

Sir now , I'm start releasing that you are doing all of this just because of views , You are saying only you are correct and rest don't know how to teach

[@BiologicArrow4]

Bhai tum sirf comment dekh ke kyu ate ho ki ye string theory me use hota he , pehele pura research karo ki, string theory me jab tum ye data lagate ho to kabhi bhi answer thik nahi ata har alag alag equation me value randomly ati he, jese quadratic me 2 root hi milenge chahe tum, real world me aply karo, kinematics me aply karo, chemistry me aply karo, ya phir struny theory me bhi aply hamesha 2 root hi milenge, but ramanujan ji ka ye method se koi bhi chiz proof nahi hoti, bas random value ati he, tum apni marzi se koi bhi infinite series lo, aur sir ki tarah common leke, check karo random value hi milengi

[@tirthbhatt8739]

Sir by respect you are wrong not totally wrong but in mathematics sir ramanujan's equation 1+2+3+4++...=-1/12 is right in rieman Zeta function rieman Zeta function use analytical method by rieman Zeta function sir ramanujan is right but by eular Zeta function sir ramanujan is wrong so this is paradox hope you read my comment sir😊

[@RaviRanjan-zu1lx]

Hardy, G.H. Divergent Series. Oxford University Press.Hardy provides a detailed discussion on divergent series and the methods used to assign finite values to them, including Ramanujan's methods.Weinberg, S. The Quantum Theory of Fields. Cambridge University Press.This text discusses the use of zeta function regularization in quantum field theory.Tao, T. An Introduction to Measure Theory. American Mathematical Society.Tao’s notes and blog often provide accessible explanations for advanced topics, including the interpretation of divergent series in modern mathematics.Summary:The expression (1 + 2 + 3 + 4 + ... = -\frac{1}{12}) is a result of advanced techniques in summation and regularization, particularly through the Riemann zeta function. It’s not incorrect but rather part of a broader mathematical framework that extends beyond elementary series summation. In appropriate contexts, this result is both valid and useful, particularly in theoretical physics and advanced mathematics.

[@avinash6922]

Bro ye series quantum M use krke toh hum sahi approximation nikalte hai syd sir ko thoda advance quantum zeta function padhna chahiye

[@sayandas5189]

​@@avinash6922ha bhai Ara ye talka sirf BTech kya hai bhai ek 4 saal k degree mai kitna tum math, physics padloge bhai? Jo phd karte hai wo pagal hai kya ? Ye 11-12th level se zada kuch nahi jante lekin bakwas 100 taka karega

[@sayandas5189]

Iss kuch advance nahi ata, agar Ata to bakwas nahi karta. Sach mai matlab ek 4 saal k degree leke phd research karne wale logo ko galat bolta hai takla

[@42xsbsrijan91]

good everning sir🙏, sir ek question maine dekha tha jisme n^n^n... infinite tak ka value diya rheta tha(for example 26 ie n^n^n...=26) aur iske solution me diya tha ki n^26=26 aur through graph iska koi point exist krta tha. So is this valid tarika? Please help me Sir!!🤔🤔🥺

[@42xsbsrijan91]

please help!!

[@mridulacharya8250]

Series of natural number is closely linked to -1/12 but the conventional sum is not that connection

[@YashKumar-ij5rc]

When you add natural numbers of 10-adic number, it comes -1/12. But when you add natural numbers in prime-adic numbers, then this chaos doesn't occur and we get infinity as our answer. The problem is with the use of 10-adic numbers. Therefore, modern scientific community and computers use prime-adic numbers for scientific theory and calculations.

[@Scientistsdm]

Distance education is best to other mode of education 🎉🎉🎉🎉 अपने को जानना हो तो खुद से padho खुद रिसर्च करो यदि mathematician बनना है तो यदि teacher बनना है या प्रोफेसर तो फिर regular ही करो 😂

[@diveshkumar6723]

Sir the sum -1/12 is found by analytical continuation of the function when you extend the input and output boundry of the function you get this value and yes this will not be used for normal day maths but for high level maths like in some high level therories of physics which discuss many diemension ie string theory etc

[@DanyalShabirr]

Sir plz reply…. How this concept is used in string theory then? They took sum of infinity = -1/12

[@BiologicArrow4]

Bhai tum sirf comment dekh ke kyu ate ho ki ye string theory me use hota he , pehele pura research karo ki, string theory me jab tum ye data lagate ho to kabhi bhi answer thik nahi ata har alag alag equation me value randomly ati he, jese quadratic me 2 root hi milenge chahe tum, real world me aply karo, kinematics me aply karo, chemistry me aply karo, ya phir struny theory me bhi aply hamesha 2 root hi milenge, but ramanujan ji ka ye method se koi bhi chiz proof nahi hoti, bas random value ati he, tum apni marzi se koi bhi infinite series lo, aur sir ki tarah common leke, check karo random value hi milengi

[@DanyalShabirr]

@@BiologicArrow4 comment dekh k nahi aaya hu… jaa k numberphilr ka video dekh ispai

[@DanyalShabirr]

@@BiologicArrow4 uspai woh bolta h ki… the results obtained are used in the calculations in the string theory

[@BiologicArrow4]

@@DanyalShabirr accha me tumse puchh ta hu ye ramanujan ka theory string theory me kaha use hota he, tumhe nahi pata, bas app bhed chal me ake ye bol rahe ho string theory me use hota he, me bata ta hu kaha use hota he, string theory me vaccum me electric field ka calculations ek scientists he hendrich kismir karke, sorry name thoda yad nahi, unke is theory me electric field me calculation ke kuch special cases me ramanujan ke -1/12 value use hota he but ajj tak koi bhi fix, always true wala result nahi mila he, or ha ye sab chiz string theory ka sirf 0.001 percent he, baki string theory me itne gazab ideas he app sunke pagal ho jaoge, app chaho to Google, quara, physicist ke videos check karo

[@DanyalShabirr]

@@BiologicArrow4 wohi toh mai bol rha hu… how can a random value be useful at some point if this random answer is merely out of mistake? I am not against the explanation given by the sir which i have already encountered it in the past. I am not in a rat race… I was just asking out of curiosity. like we know the quantization of the bosonic string involves summing over the zero point energy of each vibrational mode and that the pretty intuitive sum of these energies diverges. but using the regularization technique that assigns -1/12 to the infinite sum, the theory remains consistent and pretty well defined.

[@pradipkumarhansda9353]

Sir, it's not a little thing! because it's directly related to Riemann hypothesis through analytic continuation. ζ(s)=(2^s)(π^(s-1))(sin(πs/2))(Γ(1-s))(ζ(1-s)). if Riemann hypothesis will be proved true then, it will become 1+2+3+4+....... = -1/12. and there is one more thing- that's "1/(1-x)" series[where 0≤x

[@mrpulkit1535]

Its okay even newton said gravity is a force because it was best explaination . Then einstein said its the curvature of space

[@victorcreations424]

Actually at 12:32, s = -1\9 is correct. In mathematics there is a field in which we can generalize real numbers as infinity called p-adic number or prime adic numbers for example: Taking base 10 (it's not a prime) We consider a number Say, ......11111111 = x X is 10-adic number Now we consider another number Y = .....99999 Now we add them 1 + Y = 1 + ...9999 = ......0000 Now as there are infinite zeros, we can never approach a 1 infront of it therefore we consider 1+Y ≈ 0 Therefore ....999 + 1 = 0 ...999 = -1 ....111111 = -1/9 X = - 1\9 ...1111 can be written as an infinite series ♾️... 1000 + 100 + 10 + 1 = -1/9 1+10+100+1000 ...... ♾️ = -1/9 So that prove in 12:33 is indeed a true statement, which is applicable in real numbers generalized as consisting infinite digits. Sir, plz tell if I am wrong.

[@saurabhpatel1535]

Proof is not wrong. You can't proove that proof is not wrong

[@SwastikPadasalkar]

12:19 same proof was given in NCERT Class 10 in Mathematical Induction topic 7 years ago.

[@Arya56737]

I was going to unsubscribe, i was really angry in start, because i am fan of sir Ramanujan, but i kept my angry, ego, aside and try to listen before doing anything, i know even sir Issac newton had made mistake, he had also said that light speed is more in denser medium and less in rarer medium, if newton can make mistake why not sir Ramanujan? I like your video, it take courage sir to say wrong to someone who is already master of that field, really sir you are doing great work. Thank you.

[@siddharathdubey]

It is not usual sum which you are talking about first go and read advance mathematics and physics

[@anshul8330]

Ramanujan was NOT wrong. He himself asked a question about this result. He himself asked if an extrapolation of summation of series could be done on divergent series(just like complex numbers for real numbers)? Basically, Ramanujan also proved it and threw it as a question to mathematicians, as if asking them to invent something new. He did NOT claim the result was true for the existing Mathematics.

[@NMSPhysicsISAC]

Good to see your understanding, But of course i m talking in light of existing mathematics Cheers!!

[@NMSPhysicsISAC]

Yes we understand things on basis of our knowledge and don’t believe on “may be true”. Otherwise we have to believe everything anybody say.( perhaps i made it clear) Likhna mushkil hai

[@Divanshu-j2y]

sir , in Ramanujan series S = 1-1+1-1+1-1...... This series is not exploding to infinity . It just wobble around 0 and 1 ,so here S is not equal to infinity ,it is just any Real number .In this case we can cancel both sides of S as S is a finite number. However ,in yours series D = 1+1+1+1+1+..... which is obviously going to infinity ,so here we can not cancel out D (as infinity - infinity is not defined ) PLEASE EXPLAIN

[@sirisaacnewton69]

true but every statement may or may not have contradiction until its from godd

[@Divanshu-j2y]

@@sirisaacnewton69 matlab??

[@sirisaacnewton69]

@@Divanshu-j2y matlab bhai tu kitna bhi dimag lagale infinity based problems nahi solve hote

[@SK_Hta]

1-1+1-1+1....the sum of this series is EITHER 1 OR 0. It's not between 0 and 1.

[@naivedyam2675]

Well... The truth is this proof has been spread by youtube teachers. Ramanujan didn't actually give the value of this series. He instead gave the general formula for finding the Riemann Zeta Function for any value. Riemann Zeta Function is Z(x) = summation(1/n^x) where n goes from 1 to infinity. So, Z(1) becomes 1+1/2+1/3+... Z(2) becomes 1+1/2²+1/3²+... And so on. If you took calculus in college you would know a series of this form is convergent only for values >= 2. So, the domain of Z(x) itself is [2,infinity) But there were a few people who didn't seem to care much about the domain of functions so they started plugging in all sorts of values into the function given by Ramanujan and when they plugged in -1 they got -1/12. This is called analytic continuation in mathematics when you try to evaluate a function beyond it's domain AND THIS DOESN'T MEAN IT IS THE VALUE OF THE SERIES 1+2+3+.... A JEE student can understand this by relating to problems where you reject a solution for not satisfying the domain condition. For example let's say you were given an equation where you find x and you get the values 4 and -5. But the equation had a term log x in it so you dropped the -5 and only reported 4 because when you plug in -5 the log x term would go nuts. An algorithm only gives an output it's we who decide what values to keep and what to reject depending on the problem so plugging in the values in the original equation is crucial. This problem had a similar flaw. Ramanujan gave the formula to find Zeta function but people exploited the domain. Then there were some who created their own method to prove it is -1/12 so that general audience could understand it since they couldn't understand ramanujans formula as it involved many functions which are introduced after graduation. And that's where this proof came from. For a more detailed video on this and knowing the back story, you may checkout the video by BriTheMathGuy on the same. And yes the mistake in this solution is too trivial for someone like ramanujan so he could never come up with such a bogus approach. The first one to do so was numberphile.

[@kids_tution4890]

Sir JEE advance ke baad ab bacho ko MTH101 padha rahe. IIT me kaam aayega ye

[@aj_tech456]

Assumption :- S=infinity series Yani RHS term me hum koi bhi part me agar todte hai to wo part infinite series se chota hona chahiye.❤ S=x + y Jaha x aur y dono hi term S se chote honge

[@abirdubey5600]

No no no 1-1+1-1+1.... It is a oscillatory series it's neither convergent nor divergent and 1+1+1+1+... It is a divergent series.Ramanujan's intuition was correct

[@ayubjikani5401]

Sir, I have a suggestion for you. Have some more research on Analytic Continuation and zeros of Zeta function under complex analysis. Thank you... 🙌🏼

[@Kunalv...7554]

Naya sikhne ko to yahi mila ki koi bhi kaise bhi kisi ko glt prove kr skta hai khud glt soch ke .ramanujan ne glti nahi ki hai vo maths ke gyata hai aur vo ye glti kaise krenge

[@abhimoymukherjee89]

Wonderful explanation sir ❤❤ so fortunate to have you ❤

[@Guruvidya_academy]

Goat of maths---- ramanujan

[@yogeshtiwari9458]

यदि आप इतने ही जीनियस हैं तो अपनी बात इंटरनेशनल फोरम में रखिए और वहां कन्विन्स करिए। हम जैसे साधारण लोगों को ये अपना असाधारण ज्ञान पेलने का क्या मतलब । कुछ अच्छा सिखा सकते हो तो जरूर सिखाइये लेकिन जो आप को मालूम हो वही सिखाएं । आप को क्या लगता है कि रामानुजम जी ने ये थ्योरम श्री हार्डी जी को जब भेजा था तब वहां के गणितज्ञों ने सभी पहलुओं पर विचार न किया होगा । इस थ्योरम के बेस पर आगे बहुत काम हुआ है । आप को शर्म आनी चाहिए और इस विडिओ के लिए माफी मांगते हुए एक विडिओ अपलोड करना चाहिए। इस बात का ध्यान रखें । भ्रम न फैलाऐं ।

[@advait6057]

thank thank you soooo much sir ji.........salo se ye mujhe presan kar rha tha🙏🙏🙏

[@ashutoshdash6242]

Current doesn’t follow vector addition laws, it follows KVL and KCL. Dot products of two vectors will be a scalar( I= J.A). The definition follows mathematics and no assumptions. How can you say that you call a quantity vector/scalar as per requirement?

[@tommarvoloriddle094]

He just tries to gain views by trying to disprove famous people

[@RajaRaja-qr5us]

Infinity = continuous In series , not in parallel or branched Who can tell who has full knowledge and who knows what is happening in universe 0 means nothing Now 0/∞ is like big bang

[@gangadharchakraborty4933]

Iska matlab string theory galat hai,jiska pahela e equation hai,Nms sir sahi hai,wah wah kya sir hai

[@justsomeguywithsomememes]

Wahi to Bhai string theory me infinite natural number ke summation ko -1/12 mana gaya tha tabhi sahi result nikla tha. So string theory which has got no mistakes at all, but due to nms sir it is wrong😂😂😂😂

[@mrutyunjaymallik4068]

String Theory is not at all accepted by the mainstream scientific community, it has not been proved.

[@Gsgik431]

@@justsomeguywithsomememes ye sir to galat salat batate rahte hai bhai

[@राग-ख4ध]

​@@justsomeguywithsomememesstring theory galat है भाई 😂

[@IITJEE2025-l2t]

That's true String theory can for now be said to be WRONG! just because it has implications in string theory doesn't mean the theory itself is correct

[@adityabarnwal7666]

What an amazing myth buster... video ❤❤❤❤❤

[@adityabarnwal7666]

Thank u very much Sir to give us a new thought and mindset...❤

[@Uttam__4-c2y]

Thank you sir for clarifying, the ramanujan's mistake

[@kalingapradhan3026]

This is accepted by royal society of mathmatics

[@ujjwalverma4948]

Sir please make video on all the contributions of ramanujan in various fields

[@FizikSphere]

Before discussing this kinds of things please read some higher level physics like Quantum mechanics , quantum field theory etc. There is an application of this series to understand THE CASIMIR FORCE.. dear students don't waste your time behind these.. To understand Ramanujan We need more advanced theory of physics.. But the problem of jee teacher is that their knowledge is restricted upto 12th Standard.. standard...

[@Socrates240]

Very well sir that's great that teacher like you are still in you tube you are best teacher

[@serajmd3256]

apne jis siries par discuss Kiya hai 1/2=1-1+1-1+1-1..∞ yaha par actual me 1/2 iss series ka actual answer to nahi hai lekin iska average answer jarur hai kyuki agar app iss series ko dhayan se dekhate hai to app payenge ki(s= 1-1+1-1+1-1...∞) Iss series ke two answers hai Ya to s=1 hoga ya fir s=0 s=1 s=0 Dino ko add kar do ap payenge 2s=1 s=1/2 Yaha par 1/2 iss series ka average answer hai. ramanujan ki iss infinite series (-1/12=1+2+3..∞)ka use string theory me bhi kiya jata hai aur ye string theory me bahut important roll nibhati hai. To mujhe nahi lagta ki ye wrong hai

[@NMSPhysicsISAC]

To average answer se kya hoga. String theory mein saaf saaf likha hai analogy hai aur ye series ka sum -1/12 mathematically wrong hai

[@serajmd3256]

Me yah samjhana chahta hu ki jis tarah (s=1-1+1-1+1-1..∞ ) ka average answer 1/2 hai usi tarah (S=1+2+3+4+5...∞) ka average answer (-1/12) hoga which is also good not a bad. Main ya koi bhi ya fir koi advance quantum computer bhi infinite sum of natural number ka result nahi Bata Sakta lekin at least hame iska average to pata hai

[@IITJEE2025-l2t]

Bro its S=0 or S = 1 Not S=0 and S=1

[@VedicSanatanDharma453]

Simple definition -infinity is something which is beyond human's imagination which has no limit.

[@Veros23UK68]

Ramanuja a god gifted ❤🛐

[@New_hope_shorts]

Ramanujan sir hamare sath majak kar gaye 😅❤

[@MohitsharmaEngineer]

Sir apko Mera pranam 🙏 Sir you are my role model❤

[@sbstudios8443]

I think ∞ serieses always shows some paradoxical nature. S is ∞ series. S = ½. Let S is a series with n terms. Then n ki koii aisi value nahi aayega ki S = ½ aaye. Hence its ∞ series.

[@adityarajjadhav5006]

How you came with the conclusion in your example, 10S = 10+100+1000+.....♾️ Can you explain? How did you get the value of 10S?

[@James-o4y5y]

Rule 1 that we know: Addition of positive numbers can't be negative, so 1+2+3+......... can't be any negative quantity

[@Shivanshtiwari2025]

Yahi to maine sabse pehle socha tha❤️

[@rounakrishu]

Yes sir you are correct...

[@Desidarius_Erasmus99]

I think you should study first the books on the undergraduate texts of mathematical analysis by Walter rudin , Malik-Arora , SK Mapa . There is a famous theorem called *Riemann’s rearrangement theorem* on conditionally convergent series specifically but can also be applied on arbitrary series or any series of positive real numbers . I think you will get your answer . Mathematical analysis is one of the difficult parts in mathematics and the study of it actually makes a student a typical mathematician .

[@theinverse2853]

Sir ek video on the topic "INFINITY" it always attracts me towards itself..... And your way of explaining complex things in a simple manner is amazing... Please if you can explain THE CONCEPT OF INFINITY... HOW SCIENTISTS WORKS ON IT.... WHAT WAS THE THOUGHT OF INFINITY SCIENTIST HAVE IN THERE MIND WHILE THEY WORK ON IT ?

[@NMSPhysicsISAC]

Will try

[@virat-k9g]

Sir , can I do This , S = 1+2+3+4.......∞ = -1/12 like this S = 1+2+3+4+5+6+7+8+9+10+11+12+13...∞ as we write 1as it is , like this 1+and sum Frist three terms 1+(2+3+4)+(5+6+7)+(8+9+10)+(11+12+13).....∞ That will became 1+9+27+36+...∞ take 9 common 1+9(1+2+3...∞) and 1 +2+3...∞ is exactly is S , means that S = 1 +9s now S = -1/8 that officialy wrong I think and now -1/8,-1/12 are conflicting. So I think you are right about srinivasa ramanujan .

[@anayagrawal255]

sir you are the one who explain it correctly I have same doubt that S and S +1 is not same untill it converging series which you have clear

[@NMSPhysicsISAC]

Glad to know this. Stay tuned

[@anayagrawal255]

sure sir

[@SmithDutta-zx4qj]

Hi sir kya app Kepler ke real prove ko lekar video dal sakte hai. Asalme Kepler to newton ke paida hone ke paile hi mar gaya to Kepler ne kaise bataiya dA/dT = L/2m . Calculas to newton ne banaiya tha . Please explain in a video.please please please please Please Like and support 🙏

[@MATHS-METHOD]

without practicing of this segment you are here hats off you sir Error 10:34

[@saranshkhare2658]

Bhai mere 1-1+1-1+1..... Ka value 1/2 hota hai orr waha se sir ramanujan ke equation ko prove kiya ja sakta hai.

[@hiden6202]

Thank you sir.we need this kinds of discussions

[@NikhilSinghNirwan-ez2yh]

Sir what you are you as physics teachers and now math

[@LearnNowall]

When you consider infinity what you thing it it will be what ,on earth when you go further you sat you are going further but you will not say that you are going further. Like that .

[@mathsbyMSPSIR]

Reimann zeta function analytical conitunation is something that ramanujan talked about . and the proof is obviously wrong since the series is diverging and it is not given by ramanujan yet it is viral proof attached with the name of this great person.🙏

[@mathsbyMSPSIR]

As far as I read , I dont know much about physics ,but it is available that stephan hawking used the same function in string THEORy and quantum mechanics . you are the genius in physics and you can enlightened us with the fact. What and why he used the zeta function. Basically ramanujan was not wrong the person who first portrayed this equation in the way it is viral today is wrong . hope you get my idea. Thanks

[@mathsbyMSPSIR]

kzbin.info/www/bejne/qXWTf52YrNafj9ksi=h9lDSzQf6xIDb2mH ,this video explain analytical conitunation much better

[@mathsbyMSPSIR]

kzbin.info/www/bejne/qXWTf52YrNafj9ksi=h9lDSzQf6xIDb2mH

[@mathsbyMSPSIR]

This video shows in the end about the zeta(-1) and its analytical continuation.

[@mathsbyMSPSIR]

I have been watching your videos about those who were misguiding physics on the youtube . sir ,the proof you were talking about has nothing to deal with ramanujan . ramanujan worked on zeta function and its analytical continuation ,the irony is the expression of the continuation seems like what you have written.

[@kfaisal789]

Yeh sir to har kisi mahan insan me bhi galti nikaal denge Inka to bs kaam hi yahi hai yeh bhaisaab apne aap lo Newton ka chacha samjhte hein

[@priyanshuiit3235]

goat of physics-NMS SIR .I DONT STUDY FROM U BUT I LOVE TO WATCH YOU

[@HARI_KNOWLEDGE]

goat or god, by the way me aapko bata du ye iit jee or neet ke level se jyada level pr aaj insaan physics me tarakki kr chuka hai. plz god khke un physicist ki disrespect to mat kro jinhone apni puri life laga di in concept ko banane me, jisse aaj puri duniya ko kuch kuch na kuchh profit ho rha hai. In my view, God is one, who creates everything now some of us just finding the caluclations that god had done in his creation. foreign ki country vale kitna achha kr rhe hai aur hamri country vale mujra kr rhe hai social media pr , business kr rhe hai dusro ko kesi bhi aag me jhok kr. Everyone knows nowadays what types of business these coachings owner or Online teacher are doing.

[@ShahbazKhan-r7n7i]

Most beautiful explanation,i have ever seen❣️❣️❣️

[@yashjain9783]

Sir apne bola ke infinity ke comparison me term chota hona chahiye to wo kitna chota ho sakta (range)

[@NMSPhysicsISAC]

Infinitesimal small ( smaller than you can think of)

[@yashjain9783]

Sir matlab first term should be small as compared to infinity But 1 is also very small as compared to infinity Then why we cannot consider it

[@UMANGSRIVASTAVA]

Not wrong , this formula implement in Sting theory ,in physics this is used to prove the theory

[@jatinyadav178]

Sir you don't mention several points which should be mentioned.😊

[@iamsorry6998]

Sir, i heard his infinity sum [-1/12 ]is used in string theory

[@JangirBK]

It's all assumptions.. it's a divergent series which can be possible between minus infinity to plus infinity

[@souravkundu1898]

Fun fact: Ramanujan sir never proved it just stated that there may be a possibility that 1+2+3.. can also have value -1/12 other than infinity.

[@Baibhavprateek_]

Any batches for droppers in online for JEE?

[@NMSPhysicsISAC]

Yes we have a batch for online. Check out here - vxahy.courses.store/?mainCategory=8&subCatList=[134780]

[@Chess-kt5kq]

Agar general term ka domain extend kare toh ye thoda sense banata hai kyuki isme Bernoulli numbers ka bhi role hai aur reimann zeta function ka par us relationship ko define karna bahut kathin hoga

[@mr.kabir2.0]

First thank you sir 🙏 ki unka proof 1+2+3+....=-1/12 dikhaye , Infinite is undefined value how you let that last term is 1

[@drsknandaresearch4993]

Please don't spread wrong things. Ramanujan paradox is already proved

[@avinash6922]

Sir meri apse ek request hai aap quantum ka zeta function padhna vha pr ye approximation use ki hui hai hme lga hai vo jada better explanation hai iski or agar vo bhi daubtful hai toh aap mujhe thoda guide jarur krna taki M thoda apna level up krlu Baki aap overall kamal k teacher ho M chemist hoke bhi apke video dekh leta hu kbi kbi

[@rkchemistry5141]

Good job sir

[@somenn.s3977]

Wah Maja aa Gaya Hats off to you Sir

[@IMAN_IIT_PATNA]

Sir thanks 🙏🏻👍🏻 boht kuch sikhne ko mila sachme😊

[@IISCBANGALORE-ISMYDREAM]

Series S ek Gp thi with -1 as common ratio but for sum of infinite Gp r belongs to (-1;1) excluding both -1 and 1 so this wrong ❌

[@secretshaper7285]

Salute ur great fundamental work

[@jitendraahirwar38]

Sir what about Riemann Zeta function

[@ECGuproax99]

Ye sun lo guru ji - Ramanujan is liye bhi bhout famous Hai ki woh bhout chijo ko batate nahi the, isiliye Ye sochna ki unhe ye pata nahi hoga ki ye is tarah se galat hai, sabse badi bevakoofi hogi! 😂

[@inquisitiveminds2189]

baat toh sahi he

[@sanebrain3083]

thanku sir , kal mai issi cheez ke baare me soch rha tha

[@SathwikDonthu-qr8vd]

Wonderful explanation Neelmani sir❤

[@PramodKumar-ir3rt]

Sir it is not always true that if series last term is infinitely small then it is a conversing series .it may be conversing or diversing. As example harmoic series of nature number is a diversing series DIVERSING SERIES series that value is increasing when number of term is increased means if number of term is infinite then its value is also tending to infinity ♾️. CONVERSING SERIES series that have a finite value or when number of term is infinite then its tend to a finite value.

[@Bhagwat12356]

Good explanation sir. Now all concepts are clear

[@AzamKhan-c5u]

Sir I laterally want the answer mene bhut dhunda pr kahi nhi mila

[@ArnabDutta-w5e]

You don't have to explain it actually you got something wrong about your method without knowing actual way... How to prove it sir I love your physics teaching but don't mislead students providing them incomplete sense of maths..

[@Krishna-gm5lp]

Sir ji pranam mja aya sikhne ko bhi mila ❤❤ sir plzz guide me for jee 2025

[@pawantomar2162]

Thanku sir

[@wisdomcorner1307]

It is not a mistake Sir, it is easy to flactuate students not teachers, Can I ask you one thing, are you a phd scholar of sequence and Series, khud achha padhao Sir ap bade teacher ho, Ramanujan k theory ko ulta sidha bol k kya siddh karne ki kosis kar rahe ho aap