Sometimes the partial fraction expansion is not needed in finding the inverse Z-transform- instead the properties of the transform can be used. Consider the function F(z) = z+ 1/z^2(z - 1)
a. Determine whether F(z) is a proper rational function as a function of z and of z-1.
b. Verify that F(z) can be written as F(z) = z-2/1 - z-1 + z-3/1 - z-1. Find the inverse Z transform f[n] using the above expression.