Q1) Find power series

f(z) = e^{-z}/z^2 for 0<|z|<\infty

e^{-z} = 1 - z + z^2/2! - z^3/3! + z^4/4! ...
f(z) = 1/z^2 - 1/z + 1/2! - z/3! + z^2/4! ...

Q2)

f(z) = {1+2z^2 \over z^3 + z^5} |z|<1
     = {1 \over z^3(1+z^2)} + {2\over z(1+z^2)}

{1\over (1+z^2)} = 1 - z^2 + z^4 - z^6 ...

{1\over z^3(1+z^2)} = 1/z^3 - 1/z + z - z^3 ...
{2\over z(1+z^2)} = 2/z - 2z + 2z^3 - 2z^5 ...

f(z) =
1/z^3 + 2/z - 1/z - 2z + z + 2z^3 - z^3 - 2z^5 ...