Other geometric series that any combination of its members will yield a unique number

Question

It is understood that a geometric series such as the summation of

2⁰+2¹+2²..... all the way to infinity.

 

adding any combination of it will yield a unique member

 

Is a geometric series by definition have this as a property?

 

Is every integer greater than 1,

3⁰+3¹+3² for example have the same property?

 

I am possibly asking a very deep, complex question, but should be interesting nonetheless

Answer 1

It's a little unclear what it is exactly that you are asking. Do you mind elaborating a little on what you are looking for/interested in knowing?