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Ramanujan summation is a technique invented by the mathematician srinivasa ramanujan for assigning a value to divergent infinite series. The main tool is ramanujan's i ipx. Intuitively, the sum of all positive integers diverges to infinity

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However, ramanujan discovered a way to assign a finite value to this divergent series using techniques from. Certain infinite series are shown to satisfy simple identities between the square of the sum of the series and the sum of the squares of the terms of the series Today we are going to discuss the most popular infinite series, 1 + 2 + 3 + 4 + · · · + ∞ and its sum

Results may give your logic a shock, so be prepared.

That’s really everything this series has, and while it is my personal favourite, there isn’t a cool history or discovery story behind this However, it does open the door to proving a. Ramanujan summation is a powerful mathematical technique to assign values to certain divergent infinite series It has found applications in various areas of mathematics and.

In fact, it turns out there isn't one unique way to define the sum of infinite series that reproduces the usual sum of finitely many terms in the case where only finitely many terms in the infinite. In casimir’s solution, he uses the very sum we just proved to model the amount of energy between the plates. Ramanujan's infinite sum is not a traditional sum in the sense that it doesn't converge to a specific value It's more accurate to consider it as a result of a mathematical technique called analytic.