[Thamma]

Express $ \frac{1}{(1-z)(1-z^2)(1-z^4)} $ as a sum of partial fractions.


$ \frac{1}{(1-z)(1-z^2)(1-z^4)} = \frac{A}{1-z} + \frac{B}{(1-z)^2} + \frac{C}{(1-z)^3} + \frac{D}{1+z} +\frac{E}{(1+z)^2} + \frac{Fz+G}{1+z^2} $