Question

f（x）＝1/（x²－4X+5）展开成x-2的幂级数并求出收敛域

Answer 1

问：f（x）＝1/（x²－4X+5）展开成x-2的幂级数并求出收敛域

答：亲亲您好根据你的问题为您提供一下回答记t=x-5,展开成t的幂级数即可x=t+5f(x)=1/(x-2)(x-3)=1/(x-3)-1/(x-2)=1/(t+5-3)-1/(t+5-2)=1/(t+2)-1/(t+3)=1/[2(1+t/2)]-1/[3(1+t/3)]=1/2[1-t/2+t^2/4-t^3/8+...]-1/3[1-t/3+t^2/9-t^3/27+...]=1/6-(1/4+1/9)t+(1/8-1/27)t^3