Question

将f(x)=2x/(1+x)展成(x-1)的幂级数,并求收敛域,

Answer 1

f(x)=2x/(1+x)=(2x+2-2)/(1+x)=2-2/(1+x)

=2-2/(2+x-1)=1-1/(1+(x-1)/2)

=1-∑(n=0,+∞)(-1/2)^n(x-1)^n |x-1|