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Consider you have been given that

$$\sum_{i = 1}^{\infty}i = -\dfrac{1}{12} $$

How do you solve this sigma notation? I've not seen this kinda sigma notation before.



marked as duplicate by Namaste, Chappers, lulu, Mauro ALLEGRANZA, Lord Shark the Unknown Aug 1 '18 at 13:34

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That is the sum over $i$ of $i$, where $i\in\mathbb{N}$ goes from $1$ to $\infty$. So then that summation becomes $$\sum_{i=1}^{\infty}i = 1+2+3+\cdots$$ The result of that summation is explained by the technique of Ramanujan summation, because obviously that sum doesn't converge in the standard sense.

Most of the times to differentiate the Ramanujan summation from the standard summation we put the symbol $\Re$ somewhere over the summation sign, something like this $$\sum_{i}^{\Re}i$$


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