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Three tests for convergence of series are given which are well suited for the automatic determination of the radius of convergence of a series. The first test is similar to the standard ratio test, while the other two tests use a recurrence relation for the terms of the series. Together, these tests determine the radius of convergence of many series which arise as solutions to ordinary differential equations. Numerical examples using these tests are given.
Chang et al. (Tue,) studied this question.