You might remember from calculus that this is only true on the interval of convergence for the power series, in this case when \(|x| \lt 1\text{.}\) That is true for us, but we don't care. We are never going to plug anything in for \(x\text{,}\) so as long as there is some value of \(x\) for which the generating function and generating series agree, we are happy. And in this case we are happy.
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