(b) If f(x) has a power series representation about a point x = a with radius of convergence R > 0, i.e. ∞ f(x) = Σ c₂(x − a)" for all x € (−R + a, a + R), n=0 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-term, i.e. 00 f'(x) = Σnc₂(x − a)"-¹ for all x € (-R + a, a + R). n=0 True False

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