What is the sum of all natural numbers?
The sum of all natural numbers (1, 2, 3, 4, ...) diverges to infinity. In mathematical terms, if you try to add all natural numbers together, the result is not a finite number; it grows without bound.
However, in some contexts, particularly in certain areas of theoretical physics and mathematics, there is a concept known as "regularization" that assigns a value to this infinite series. One famous result is that the sum of all natural numbers can be associated with (-\frac{1}{12}) through a process called analytic continuation, specifically in the context of the Riemann zeta function.
It's important to note that this result does not mean that the actual sum of all natural numbers is (-\frac{1}{12}) in the traditional sense; rather, it is a value that emerges from a specific mathematical framework. In standard arithmetic, the sum of all natural numbers is simply infinite.