设f(x)=1/(x^2+3x+2),将f(x)展开成（x-1)的幂级数
人气：339 ℃ 时间：2020-07-17 03:58:27
解答
记t=x-1,则x=t+1f(x)=1/(x+1)(x+2)=1/(x+1)-1/(x+2)=1/(t+2)-1/(t+3)=(1/2)/(1+t/2)-(1/3)/(1+t/3)=(1/2)[1-t/2+t²/4-t^3/8+..]-(1/3)[1-t/3+t²/9-t^3/27+...]=1/6-t(1/4-1/9)+t²(1/8-1/27)-t^3(1/16...
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