将函数f(x)=1/(x-1)(x-2)展开成x的幂级数,

Question

将函数f(x)=1/(x-1)(x-2)展开成x的幂级数,

Answer 1

f(x)=1/(x-2)-1/(x-1)
=-0.5/(1-x/2)+1/(1-x)
=-0.5[1+x/2+x^2/2^2+..+x^n/2^n+...]+[1+x+x^2+.+x^n+...]
=0.5+3/4*x+...+[1-1/2^(n+1)]x^n+...
收敛域为|x|