The task says: Find generating function for a series $a_n$ ($ n \geq 0$) where $a_n$ is subsets of some $n$-memeber set
I tried to solve it but couldn't so I looked in solutions, this is a solution
$$a_n=2^n \qquad f(x)=\sum_{n \geq 0} 2^nx^n=\frac{1}{1-2x}.$$
What I don't understand is, why is $ a_n = 2^n $?
Thanks for help!
