将函数f(x)=1/(x^2-2x-3) 展成x的幂级数,并写出收敛域_数学解答

将函数f(x)=1/(x^2-2x-3) 展成x的幂级数,并写出收敛域

人气：312 ℃　时间：2020-05-22 07:21:10

解答

f(x) = 1/(x² -2x+3) = 1/[(x-3)(x+1)] = -1/4 [1/(x+1) + 1/(3-x) ]
1/(x+1) = ∑ (-1)^(n-1) x^(n-1) ,-1