[dmlerner]

1 + 2 + 3 + ... = -1/12 total beers

-1/12 beers * $3 / beer = -$0.25

negative -> pay them for taking the beer

The -1/12 result is pretty widely known, but not particularly true. It's called "analytic continuation." There's a nonrigorous proof that's accessible at a highschool level - see [here](https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...)

Delightfully, this comes up in string theory, in computing the dimensionality of spacetime.