将函数(2x+1)/(x²+x-2)展开成x-2的幂级数,并指出其收敛区间

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令t=x-2,则x=t+2,展开为t的幂级数即可
(2x+1)/(x^2+x-2)
=(x+2+x-1)/[(x+2)(x-1)]
=1/(x+2)+1/(x-1)
=1/(t+4)+1/(t+1)
=1/4*1/(1+t/4)+1/(1+t)
=1/4[1-t/4+t^2/4^2-t^3/4^3+...]+[1-t+t^2-t^3+...],收敛区间为|t/4|