设f(x)=x/(2x^2+7x-4)在x0=-1处展开成幂级数,并求其收敛域

设f(x)=x/(2x^2+7x-4)在x0=-1处展开成幂级数,并求其收敛域

f(x) = x/(2x^2+7x-4)
= (1/9)[1/(2x-1)]+(4/9)[1/(x+4)]
= (-1/27){1/[1-(2/3)(x+1)]}+(4/27){1/[1+(1/3)(x+1)]}
= (-1/27)Σ[(2/3)(x+1)]^n+(4/27)Σ[-(1/3)(x+1)]^n
= …,|x+1|