Question

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?

Answer 1

• Three beers.

Explanation:

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:
  `1,(1)/(2), (1)/(4), (1)/(8), (1)/(16) \cdots`

• 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
  `6,2,(2)/(3), \cdots`

• 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.