Is Ramanujan summation true?

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. …

What is sum of all natural numbers?

This is simple arithmetic progression. A Sum of natural numbers from 1 to n. The answer is n(n+1)/2. So, if ‘n’ were to tend to infinity, summation should tend to infinity.

What happens when you add up all the natural numbers?

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.

Is the sum of all natural numbers always 1 / 12?

The way to regularize the sum is by no means unique, but the finite part of the sum is always -1/12. Originally Answered: What is the sum of all natural numbers and its proof? -1/12 is the correct answer. Don’t believe me? Keep reading to find out how I prove this, by proving two equally crazy claims:

Is the sum of natural numbers up to infinity?

A Sum of natural numbers from 1 to n. The answer is n (n+1)/2. Atleast, this is what we were taught all throughout our schooling. So, if ‘n’ were to tend to infinity, summation should tend to infinity.

Is the sum of all natural numbers negative?

So far, the consensus seems to be negative. A fairly well-known (and perplexing) fact is that the sum of all natural numbers is -1/12. No, this is not true. It can, if you really want, be seen as an assigned value to a divergent series. – Eff Jul 25 ’16 at 20:45

How to regularize the sum of all natural numbers?

Following is one way we can regularize the sum. This is how we retrieve a regularized finite part from the divergent summation. The way to regularize the sum is by no means unique, but the finite part of the sum is always -1/12. Originally Answered: What is the sum of all natural numbers and its proof? -1/12 is the correct answer. Don’t believe me?