From: "Gerben Dirksen"

Theorem:
1 + 2 + 4 + 8 + 16 + ... = -1

It is well known that in computers the number -1 is represented by FFFFFFFF (hexadecimal) or 1 + 2 + 4 + 8 + 16 + ...

Proof:

Let x = 1 + 2 + 4 + 8 + 16 + ...

=> 2x = 2 + 4 + 8 + 16 + ...
-------------------------------- -
-x = 1

x = -1