The Brain-Melting Weirdness of Infinite Series

Phil Plait of Slate's "Bad Astronomy" blog got so much flak for a post about a series of positive integers summing to a negative fraction that he did a follow-up.

In the second post—part correction, part apology, part ode to the intricacies of mathematics—Plait quotes "the delightful mathematician Jordan Ellenberg," makes a plug for analytic continuation, and cautions against manipulating series without due circumspection.