Question

将f(x)=x|x*x+x-2展开成x的幂级数

Answer 1

先将展开成部分分式

f(x)= -1/3*1/(1-x)+2/3*1/(1+x)

那么1/(1-x)和1/(1+x)会展开吧

下略

x/(x^2+x-2)=-(x/2) - x^2/4 - (3 x^3)/8 - (5 x^4)/16 - (11 x^5)/32 - (21 x^6)/64 - (43 x^7)/128 - (85 x^8)/256 - (171 x^9)/512 - (341 x^10)/1024+o[x]^11