f(x)=1/(x^2-1)=1/2[1/(x-1) -1/(x+1)]=-1/2[-1/(x-1) +1/(x+1)]1/(1-x) 展开为∑x^n1/(x+1)展开为∑(-1)^n *x^n n从0开始相加得=-1/2[∑x^n +∑(-1)^n *x^n ]=-∑x^(2n)收敛域为(-1,1)