Ramanujan: The New Sum of All Natural Numbers

Abstract

As we know that Sir Ramanujan gave the solution of sum of all natural numbers up to infinity and said that the sum of all natural numbers till infinity is -1/12. I studied on this topic and found that if we try to solve the infinite series in a slightly different way, then we get the answer of its sum different from -1/12, so this is what I have written in this paper that such Ramanujan Sir, what was the mistake in solving the infinite series, which by solving it in a slightly different way from the same concept, we get different answers.

Introduction

Conclusion

Here we\'re seeing withinside the very last end result that simply extrade the technique of calculating your sum, so we get the solution 1/12 alternatively of -1/12. Now the query arises why is that this happening? So let\'s apprehend why that is happening. As we see withinside the equation that to get our answer, we\'ve taken into consideration an equation(2) that\'s incomplete in itself and base 0, therefore, for one of these equation whose base is 0 and which will fill us with further error which is clearly visible to us.

References

[1] Ramanujan summation https://en.wikipedia.org/wiki/Ramanujan_summation [2] Mark Dodds https://www.cantorsparadise.com/the-ramanujan-summation-1-2-3-1-12-a8cc23dea793 [3] https://www.iitk.ac.in/ime/MBA_IITK/avantgarde/?p=1417 [4] A.M.s. (2016). Contributions of Srinivasa Ramanujan to Number Theory. Bulletin of Kerala Mathematics Association. 13. 259-265. [5] Taneja, Inder. (2017). Hardy-Ramanujan Number -1729. RGMIA - Research Report Collection. 20. 1-50.

Copyright

Copyright © 2022 Gaurav Singh Patel, Saurabh Kumar Gautam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.