Question

求下面级数的收敛域

Answer 1

=∑((x－1)/(x+1))^n/(2n－1)
令t=√(x－1)/(x+1)
=t∑t^(2n－1)/(2n－1)
=t∫∑t^(2n－2)dt
=t∫1/(1－t²)dt
=t/2∫1/(1+t)+1/(1－t)dt
=(t/2)(ln(1+t)－ln(1－t))