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by qmalzp 3120 days ago
Tl;Dr

It's slightly more accurate to say if

F(s) = 1^s + 2^s + 3^s + ...

Then

F(1) = -1/12.

This is still a lie, but the truth is that F(s) does make sense for a large domain of s, and there is a unique and canonical way of extending F(s) to a larger domain which contains 1. And then that new function evaluated at 1 is equal to -1/12.