Finding The Radius of Convergence
Two cases arise. The first case is theoretical: when you know all the coefficients then you take certain limits and find the precise radius of convergence. The second case is practical: when you construct a power series solution of a difficult problems you typically will only know a finite number of terms in a power series, anywhere from a couple of terms to a hundred terms. In this second case, extrapolating a plot estimates the radius of convergence.
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