Please help with practice problem.

For each of the questions below, indicate if the statement is true (T) or false (F). (a) Every power series converges somewhere. (b) If f (x) has a power series representation about a point x = a with radius of convergence R > 0, i.e. 00 f(x) = Zena a)\" forallx e (R + 030 + R), n20 then a power series for f ' (x) about the point x = a with the same radius of convergence R can be obtained by differentiating the power series for f (x) term-by-terrn, i.e. oo f'(x) = 2 ncn(x (3H for all x e (R + a,a + R). n:0