求arctan(2x/2-x^2)的麦克劳林级数,求详解
问题描述：
求arctan(2x/2-x^2)的麦克劳林级数,求详解
答
arctan(2x/2-x^2)求导得：1/[1+(4x^2/(2-x^2)^2]=(2-x^2)^2/[(2-x^2)^2+4x^2]=(4-4x^2+x^4)/(4+x^4)=4/(4+x^4)-4x^2/(4+x^4)+x^4/(4+x^4)=1/(1+x^4/4)-x^2/(1+x^4/4)+(1/4)*x^4/(1+x^4/4)=Σ(-1)^nx^(4n)/4^n-x^2Σ(...