Thank you so much. True / False If the radius of convergence of sigma^infinity_n

Question

Thank you so much. True / False
If the radius of convergence of sigma^infinity_n = 0 c_n x^n is 3, then the interval of convergence is [-3, 3]. If the radius of convergence of sigma^infinity_n = 0 c_n x^n is 3, then the interval of convergence includes (-3, 3) If the radius of convergence of sigma^infinity_n = 0 c_n x^n is 0, then the series converges only for x = 0 It is possible for the interval of convergence of a power series sigma^infinity_n = 0 a_n x^n to be (-1, 3]. If the radius of convergence of sigma a_n x^n is 2, then so is the radius of convergence of sigma a_n nx^n - 1. For all real numbers x, 1/1 - x = sigma^infinity_n - 0 x^n. If -1

Explanation / Answer

1. False. The series may not converge at equality.

2. True

3. True

4. False . R <Ia I

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