Question

x/(4-x^2)^2 幂级数展开 并求收敛域半径

Answer 1

f(x)=x/(4-x^2)^2 f(0)=0

∫f(x)dx=(1/2)∫1/(4-x^2)^2dx^2=(-1/2)/(4-x^2)

=(-1/8)/(1-x^2/4)=∑(0,+∞)(-1/8)(x/2)^n |x/2|