Question

Consider the function arctan(x/6)arctan⁡(x/6). write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. for example, if the series were ∑∞n=03nx2n∑n=0∞3nx2n, you would write 1+3x2+32x4+33x6+34x81+3x2+32x4+33x6+34x8. also indicate the radius of convergence.

Answer 1

(x^2)/36 - (x^4)/1944 + (23x^6)/2099520 - (11x^8)/44089920 + (563x^10)/95234227200 radius of convergence = DNE (the series does not converge)