数学问题求解 将该函数fx在x=1处展开成幂级数,并求其收敛区间

2025-03-20 06:10:22
推荐回答(1个)
回答1:

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