Question

求这个幂级数的收敛区间∞∑n=0 (-1)^n/(2n+1)乘以(x-1)^(2n+1)

Answer 1

设un(x)=[(-1)^n/(2n+1)](x-1)^(2n+1)

则u(n+1)(x)=[(-1)^(n+1)/(2n+3)](x-1)^(2n+3)

因为ρ=lim|u(n+1)(x)/un(x)|=lim|(2n+1)/(2n+3)||x-1|^2=|x-1|^2

当ρ