People laugh at a mathematician who says that he can give mo

People laugh at a mathematician who says that he can give money to an infinte number of people if the first person takes $100 and each subsequent person takes one half of the earlier person. Is it really possible for this to be done without going bankrupt?

Solution

The mathematician claims to be able to give money to an infinite number of people if the first person takes $100 and the subsequent person is given half the amount.

The amount that is being given out is 100, 50, 25, 12.5, 6.25 ...

This is a geometric series with first term a = 100 and common ratio r = (1/2). The sum of an infinite terms of a geometric series with common ratio less than one is [S_oo = a/(1 - r)] . The total amount that the mathematician has to give out is only equal to [100/(1 - 1/2)] = 2*100 = 200.

The mathematician can do what he claims if he has $200 with himself.