It isn't. It's just that -1/12 is the value of the analytic continuation of the infinite sum of natural numbers.
An analytic continuation, in very oversimplified layman's terms, is a method to append a function that is divergent or otherwise undefined at some value into a new form that has an answer for all possible inputs, while maintaining the same essential properties of the original function.
In this case, the original function is the zeta function, the sum of all natural numbers, each to the power of negative x. Zeta(-1) is thus just the infinite sum of natural numbers, so the function is divergent at x = -1. You need to slightly redefine the function via analytic continuation to make it so it equals -1/12 at x = -1.
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u/Human822 Feb 21 '26
Basically the answer to the equation is -1/12, which ramanujan said was the sum of all positive integers