Question

EXAMPLE 7 Find a power series representation for f(x) = arccot(x). SOLUTION We observe that f'(x) = -1/(1 + x2) and find the required series by integrating the power series for -1/(1 + x2). -1 arccot(x) = S — - dx (1 + x2) = S-1 - + x4 * + ...)dx = C - X+ To find C, we put x = 0 and obtain C = arccot(0) = n/2. Therefore = 1/2 - x + - + 00 (-1) = n/2 - n=0 Since the radius of convergence of the series for -1/(1 + x2) is , the radius of convergence of this series is also

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