f(z)=1-2/(z+2)=1-1/[1+(z/2)]=1-1/[1-(-z/2)],根据1/(1-z)=1+z+z^2+...,所以
f(z)=z/2-z^2/2^2+z^3/2^3-...+(-1)^(n*z^n/2^n),z的绝对值没错，而1/(1-z)=1+z+z^2+...的要求是|z|<1，所以这里|-z/2|<1即|z|<2