Show with generating functions that every positive integer has a unique decimal representation.
I've come up with the following to represent the ones, tens, hundreds, so on:
I then get this for my generating function:
Even then, I'm not sure if I'm doing the problem correctly.
Just realized that the terms cancel out so I get:
I'm stuck here now. I know I need to get something like $12 = 1*10^1 + 2*10^0$, but I don't know how to do that with generating functions.