I attached the theorem that is supposed to be used for the question below

2 Theorem If the power series _ on (x - a)" has radius of convergence R > 0, then the function f defined by f (a) = co + c1 (2 - a) + c2(2 - a)' +...= cn(2 - a) " n=0 is differentiable (and therefore continuous) on the interval (a - R, a + R) and (1) f' ( ac) = 1 + 2c2 (2 - a) + 3c3(x - a) + ...= nen(2 - a) -1 n=1 (ii) [ f (x) dac = C + co (x - a)tc (2-a) (x-a) 3 2 + C2 3 + ... = C+ En-0 Cn (x-a) n+1 n+1 The radii of convergence of the power series in Equations (i) and (ii) are both R.2. Using methods of section 11.9, find the power series representation of f(x) = In(1 + x2) and the corresponding radius of convergence. Hints: more than one method is needed, and theorem 2 will be of great help