A very wrong proof once showed that the sum of all positive integers (1 + 2 + 3 + 4...) was -1/12. In reality, the infinite sum has no solution, so this proof became something of a meme.
Technically technically, in some number fields (not the natural numbers) it is correct, but since it doesn't apply to all number systems it's incorrect to say it's the answer without also specifying you're using a nonstandard number system.
As someone else said, it's used in quantum physics where a lot of fancy math is used in complex number fields.
TL;DR: in some interpretations, 1 + 2 + 3 + … equals to -1/12. This interpretation has actually found some uses in physics. In general, this is not widely accepted as it depends on a specialized meaning of the equals sign. It shouldn’t be used unless you really know what you’re doing.
I don't like the Ramanujan explanation at all because c - 4c doesn't equal the divergent series, since 4c is only supposed to subtract from every other number, so it has more terms at every single limit of n, and thus more terms at infinity. So c - 4c is just -3c, not a divergent series.