应是 f(x) = 3x/(x^2+x-2) 吧。f(x) = 3x/(x^2+x-2) = 3x/[(x-1)(x+2)] = 1/(x-1) + 2/(x+2)= 1/(1+x-2) + 2/(4+x-2) = 1/(1+x-2) + (1/2)/[1+(x-2)/4]= ∑(-1)^n (x-2)^n + (1/2)∑(-1)^n [(x-2)/4]^n= ∑(-1)^n[1+1/2^(2n+1)](x-2)^n收敛域 -1
