高数 将函数展开成麦克劳林级数

1) 1/(x^2-3x+2)=1/[(x-1)(x-2)]=1/(x-2)-1/(x-1)
=-1/2*1/(1-x/2)+1/(1-x)
=-1/2*[1+x/2+x^2/2^2+...+x^n/2^n+..]+[1+x+x^2+..+x^n+..]
=1/2+(1-1/2^2)x+(1-1/2^3)x^2+.
2)因为e^x=1+x+x^2/2!+..x^n/n!+...
xe^(-x^2)=x*[1-x^2+x^4/2!-x^6/3!+...]=x-x^3+x^5/2!-x^7/3!+.