Question

f(z)=1/(z^2+5z+6)在z=0的幂级数展开式的收敛半径为

Answer 1

f(z)=1/(z^2+5z+6)

=1/(z+2)-1/(z+3)

=(1/2)/(1+z/2)-(1/3)/(1+z/3)

=(1/2)∑(n=0,+∞)(-z/2)^n-(1/3)∑(n=0,+∞)(-z/3)^n

=∑(n=0,+∞)(-1)^n(1/2^(n+1)-1/3^(n+1))z^n |z|