There is a math joke that floats around the internet every once in a while that goes something like . . . A mathematician and her infinitely many friends decide to stop by their favorite bar. The first mathematician orders 1 beer, the second orders 1/2 a beer, the third orders 1/4 a beer, the fourth orders 1/8 a beer, the fifth orders 1/16 a beer. . . it’s at this point the bartender, knowing a little math herself, interrupts and says "Fine, I’ll just pour you two beers.". How many beers should the bartender pour if the first mathematician orders 6 beers, the second orders 2 beer, the third orders 2/3 a beer, and so on?