"Benderama" is an episode of Futurama, which aired on June 23, 2011. Part of the episode was read by the Futurama voice actors at the San Diego Comic Con.
The Professor invents a machine that takes in any object and creates two half-sized copies, consuming matter provided to it in order to do so. He uses the machine to create a number of sweaters suited to his shrunken, old-aged self and sets Bender on the task of folding them. Bender looks for a shortcut and creates duplicates of himself using the machine to do the job for him. This soon escalates and eventually there are trillions of increasingly smaller copies of Bender creating copies of themselves until eventually they threaten to consume all of the matter on Earth.
Professor Hubert J. Farnsworth invents a machine that can scan an object and produce two smaller copies, consuming matter provided to it in the process. He uses it to make smaller sweaters for himself, since he is shrinking and feeling colder as he ages. Bender Bending Rodríguez originally refuses the professor's request to fold them, then stuffs the replicator into his chest cavity and uses it to make two duplicates of himself so they can each fold one sweater. Before they can do so, the Planet Express Crew (including the two new Benders) is sent to deliver a shipment of personal hygiene products to an ugly, giant alien humanoid who lives in a cave. He endures the crew's comments about his appearance until Fry inadvertently insults his mother, causing him to lash out and nearly destroy the ship before it escapes.
Back on Earth, Bender's two duplicates laugh about the funny comments they made until Bender wants some cigars. So They copy themselves in order to get four cigars for Bender. The process continues until there are 11 generations of Benders running around the office: the crew quickly moves in to exterminate all the duplicates, but Amy discovers that one of them has escaped. As this one gives rise to a new swarm that keeps reproducing and consuming matter, including Bender's couch and beer, the Professor worries that they will eventually eat the Earth. Leela points out that since the Benders are fueled by alcohol, they will run out of power once they have used up the planet's supply. When this happens, the crew sweeps up the Benders and flushes them down the toilet.
As the Professor takes a bath, he is surprised to find that the water in the tub has turned into alcohol. Some of the Benders survived and have reached the atomic/molecular scale, where they can synthesize alcohol directly from water and carbon dioxide molecules. As a result, the entire population of Earth becomes extremely drunk and the planet's fresh water supply is gone. At this point, the giant alien arrives on Earth to apologize for his earlier outburst, even though the crew keeps insulting him and Zapp Brannigan tries to destroy him with a tank. Unable to get hold of the therapist who has been helping him deal with his anger issues, the alien flies into another rage and starts tearing up the city. Bender, the only sober crew member, agrees to fight the alien if Fry will fold the Professor's two sweaters. Bender uses the hordes of tiny duplicates to form "Big Bender" and fight the alien hand-to-hand. He loses the fight after insulting the alien's mother, but the swarm quickly consumes the alien to leave only dust. Bender urges them to help him solve other worldwide problems, but they are too lazy to take part and leave Earth instead.
As the other crew members recover from a terrible hangover the next morning, the Professor is happy to note that someone finally folded his sweaters. When Fry asks Bender if he did this and learned a lesson about being lazy, Bender cryptically replies that perhaps he did - or perhaps he kept one of the mini-Benders around to do the job for him. He then exhales cigar smoke, which turns out to be composed of thousands of microscopic, maniacally laughing Benders.
The first act of the episode was read by the show's voice actors at Futurama's 2010 San Diego Comic Con panel.
The formula that the Professor shows representing the mass of the successive generations of Bender is an iteration of the Harmonic Series, which is divergent. This means that the sum of all generations gets larger without limit and that it would be theoretically possible for the combined mass of all the Benders to be infinite.