Finding a probability on an infinite set of numbers I have $\Omega={1,2,3,...}$ and the possibility of each number is $P(A) = 2^{-n}$, $n=1,2,3...$
I have to prove $P(\Omega) = 1$ . I can understand that from the graph, but how do I actually prove it?

$P(Ω) = \sum_{n=1}^{\infty} P(n) = \sum_{n=1}^{\infty} 2^{-n} = \frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3} + ..... = \frac{1/2}{1-1/2} =1 $
