Is Ramanujan Summation Correct?

Although the Ramanujan summation of a divergent series

is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.

How can Ramanujan summation be true?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.

Where is the Ramanujan sum used?

Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently-large odd number is the sum of three primes.