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?

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. . .

The Sequence is: [tex]1,\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} \cdots[/tex]

On observation, the next term is derived through the division of the previous term by 2.
2 is the constant factor
Therefore, the bartender says 'Fine, I’ll just pour you two beers.'

Therefore, if the first mathematician orders 6 beers, the second orders 2 beer, the third orders 2/3 a beer, and so on

The sequence is [tex]6,2,\frac{2}{3}, \cdots[/tex]

On observation, the next term is derived through the division of the previous term by 3.
3 is the constant factor
Therefore, the bartender should pour three beers.