Power Series ArcTan??? 1. The problem statement, all variables and given/known data Let f be the function given by f(t) = 4/(1+t^2) and G be the function given by G(x)= Integral from 0 to x of f(t)dt. A) Find the first four nonzero terms and the general term for the power series expansion of f(t) about x=0. B) Find the first four nonzero terms and the general term for the power series expansion of G(t) about x=0. C) Find the interval of convergence of the power series in part (B). Show the analysis that leads to your conclusion. 2. Relevant equations d/dtArctan(t)=1/(1+t^2) 3. The attempt at a solution A) a=4, R=-t^2. f(t)=Sum from n=1 to infinity of 4 * (-1)^n * t^2n First four terms: -4t^2 + 4t^4 - 4t^6 + 4t^8 B) Integral from 0 to x of 4/(1+t^2)dt = 4arctan(t) from 0 to x = 4arctan(x) Now I don't know where to go from here. I don't know how to write the power series for the antiderivative of the original power series, since it is not in the standard form of a power series. Can anybody help?