Are all geometric series power series?

Question

From the general equation of both geometric and power series, the only difference I see is that power series have varying coefficients and can be centered around a non 0 point whereas geometric series stick with a first term, so are all geometric series, power series? [I used series as in the terms of the series or in another sense the terms of the corresponding sequence]

Answer 1

My take on this: in a geometric series, the powers of a fixed quantity- let's call it β- are summed.

You can make a power series by letting the thing that's being raised to powers vary. Maybe that's what you're talking about? And sure, Σ^∞_n=0 xⁿ converges for x ∈ (0,1)

So yes, that's a special case of a power series. But power series are much more general- e.g., Taylor series