51. It is possible for a power series to have a radius of convergence of zero. Such a series is worthless in practice, s

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51 It Is Possible For A Power Series To Have A Radius Of Convergence Of Zero Such A Series Is Worthless In Practice S 1 (45.69 KiB) Viewed 23 times

51. It is possible for a power series to have a radius of convergence of zero. Such a series is worthless in practice, since it is a function whose domain consists of a single point. a) Verify that the power series (n!)x” converges only when x = 0. b) Is it possible for a power series to diverge at every real number? 52. a) I stated earlier that a Taylor series is a special "breed" of power series. Explain why this is true. b) Find the intervals of convergence for the Maclaurin series of sin x, cos x, 1/(1 - x), and In(1 + x).