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Questions tagged [ramanujan-summation]

Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to infinite divergent series.

Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to infinite divergent series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined. It is like a bridge between summation and integration.

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Grandi's series

So a couple of days ago I decided to learn why Ramanujan's theory 1+2+3+4+... = -1/12 is the way it is. The first step in the proof/derivation was to consider Grandi's series A = (1-1+1-1+1-1+1-1...) and how he "manipulated" it. The first thing he…
Glace
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Ramanujan summation Series

I am a class 12 student and I am Wondering about the Ramanujan summation Series that is 1+2+3+..... = -1/12. As per my knowledge Summation of positive number gives a positive number but in the Ramanujan summation Series value is negative. Can you…
Tips
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Which Ramanujan's formula used the biggest constants?

After the first time I saw the movie "The Man Who Knew Infinity", about Srinivasa Ramanujan, I've looked up some of his formulas on the web. One of such formulas amazed me the most, because it used three really big integers (like 10 to 20 digits…
Rodrigo
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What does $1+2+3+...=-\frac{1}{12}$ mean?

I do understand and am able to reproduce the steps to proove that $$1+2+3+...=-\frac{1}{12}$$ as, for example, shown in the Numberphile YouTube video. I can proove it, but I can't understand it. My brain is unwilling to accept that a series $a =…
Markus Appel
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Significance of the Ramanujan summation

I wanted to know how the Ramanujan series works only using basic calculus. Why is it a shocking fact for the sum of an infinite series to be $-\frac1{12}$? How is it important to us and how does it change our perspective towards mathematics? Have…
b_boundary
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The sum of the series $\sum_{n=9}^{\infty}\frac{1}{\sqrt(N)}$

Proving that the sum of $\sum_{n=9}^{\infty}\frac{1}{\sqrt(N)}= -\frac{1}{\sqrt(3)}$ Hi, I am trying to proving the sum above where $N$ is all the odd composites , any hint please ?
Shopify lover
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