I was watching Futurama and in a recent episode, the professor creates a duplication machine.
The machine basically took something and then made 2 copies at 60% the size.
Somehow Bender got caught in the machine and he started duplicating infinitely.
The problem is, Bender needed excess matter to create these duplicates.
The professor then reveals this equation which would explain why it was a threat to the universe as the ammount of matter needed to create the excess bending units would never converge to 0 thus, eventually, needing the entire mass of the universe to keep the series going:
This was already asked on SciFi.SE, but I'm still confused as to what this equation is actually saying. And how it is divergent.
Or if it is even accurate in it's concept.
(1) The situation you describe (2 copies at 60% the mass) is a divergent series.
(2) The sum in the picture linked above is also divergent -- it's harmonic.
(3) The sum in the picture does not represent the situation you describe. For that, the sum would look like
$$M = \sum_{n=0}^\infty 2^n M_0 (0.6)^n$$
which is a divergent geometric series.
(4) The head writer on Futurama studied physics at Harvard and CS at Berkeley, has published math papers, and earlier episodes of Futurama have featured much more sophisticated math than this, so it's likely that the equation displayed above accurately represents the situation described in the show. I'll have to try to catch a rerun and see exactly what Farnsworth says.