Sometimes the ratio test (Theorem 2) can be applied to a

Chapter 8, Problem 7E

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Sometimes the ratio test (Theorem 2) can be applied to a power series containing an infinite number of zero coefficients, provided the zero pattern is regular. Use Theorem 2 to show, for example, that the series has a radius of convergence if and that has a radius of convergence if [Hint: Let z = x2]

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