Are all geometric series...power series? Will someone explain, in lamen's terms, why this is true or not true?

It depends on your definitions... A power series is a series of the form a_0 + a_1*x + a_2*x^2 + ... or the sum of i from i=0 to infinity of a_i*x^i. A geometric series has a very similar form, being the series a_r*x^r for r = 0 to infinity (or any other number really, it needn't be infinite), but here, the x is considered a constant usually; so I guess the answers might be that geometric series needn't go to infinity, whereas power series kind of usually do (especially if they are power series approximations to non-polynomial functions, in which case they invariable have an infinite number of terms), and also power series are usually functions where as geometric series can be considered functions but are usually numerical quantities. However, geometric series can be modelled by power functions if you choose. Hope this helps :)