>>11399851It all hinges on how you approach infinite addition. The sum in the left hand sign of your equation actually diverges to infinity.
However you can also define a certain function (the Riemann zeta function) such that this left-hand term would be the value of that function at 1 (so zeta(1) = your left-hand term).
There is still an issue precisely because you can't define a standard function at a point where its value would be infinity. However you can define it in the standard way anywhere around that point.
Now analysis has plenty of way to understand the behavior of a function at a point given its behavior all around that point. In particular it allows you to "complete" the value of a function at a point where it isn't traditionally defined, provided it is properly defined all around that point, and provided certains conditions are met. This is called analytic continuation.
In the case of the Riemann zeta function at 1, the completion yields -1/12.
So it's not easy to explain in layman terms, but basically the equality you've written in your OP rests on an abuse of language and is a bit misleading. However it would be in essence correct if you added the proper qualifications about what the sign "=" means here. Namely, it's not an "=" in the traditional equality between numbers, it denotes an analytic continuation.
