4. We have seen in lectures that the differentiation of a function given by valid power series expansion can be carried out termwisely on the power series. Now we turn to study the integration. Suppose that the radius of convergence of the power series f(2) = Lar(z – z0)* k=0 is R, R> 0. (a) Show that the power series ak F(2) = L+1= - z0)*+! k=0 is at least R and that F'(z) = f(z) for all z with |z – zo| < R.

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