A mathematician organizes a raffle

A mathematician organizes a raffle in which the prize is an infinite amount of money paid over an infinite amount of time.

Of course, with the promise of such a prize, his tickets sell like hot cake. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment:

“1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that…”