Consider the Maclaurin series g(x)=n=1∑∞2n−1(−1)n+1x2n−1.
(a) Determine the radius of convergence of the series for g.
(b) Derive a power series representation for an antiderivative G(x) of g that satisfies G(0)=0.
(c) Determine the radius of convergence of the series obtained in part (b).
(d) Test the convergence of the series for G at the endpoints of its interval of convergence and state the full interval of convergence.
a. Part (a)
b. Part (b)
c. Part (c)
d. Part (d)