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Is this an antijoke or did I just need to know where it's going, like the bartender? Maybe the bartender is confused?

The joke is that the Ramanujan sum of 1 + 2 + 3 + 4 + ... is equal to -1/12, so the check should be $3 * -1/12 = minus one quarter. [0]

Thanks, that's a bit of math trivia I either forgot or never learned.

This joke relies on the listener knowing that the regularized sum of 1+2+3+... = -1/12.

That's what makes it funny!