A geometric series is one having a common ratio, right? Something like:
$$\sum_{n=0}^{\infty} ar^n$$
And a power series is one with the form:
$$\sum_{n=0}^{\infty} c_n(x-a)^n$$
Initially, I thought a geometric power series was one which had a rational function in $x-a$; something like $\frac{x}{2}$ with $a=0$, or maybe $\frac{x-a}{n}$.
But, you can think of the expression $(x-a)$ as a rational function of the form:
$$\frac{(x-a)}{1}$$
So, does that mean all power series (for $x$ within a radius of convergence) are geometric series? It seems so, but I don't want any misconceptions in my understanding, so I thought it best to ask.
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