I'm trying to take the (two-sided, aka defined for all n) Z-transform of What I tried to do was split x(n) into But a problem arises now because the z-transform of the first equals the negative of z-transform of the second, which makes the z-transform = 0. Waaah? Could this be?
I dont think the z transform would exist.The right sided sequence will converge only when magnitude of z is greater than 1 and left sided sequence will converge only when z magnitude is lesser than 1 and hence the whole series is not summable .