FIR filter : $h(n)$ is palindrome? I study condition for fix if filter is a linear phase,but it's not clear in my mind!

I have this $h(n)$:
$$h(n) = \begin{cases} \left(\frac{1}{2}\right)^{n} &amp; 0&lt;n&lt;N-1 \\[2ex] 0 &amp; \text{elsewhere} \end{cases}$$
I got the $H(z)$: 
$$
H(z) = \frac {\left(\frac{1}{2}\right)^{N}{z}^{-N}-1}{\frac{1}{2}{z}^{-1}-1}
$$
Now, for the phase linear what I do ? I think to verify palindrome property for this $h(n)$, but how ?? or I can finally say that to the form that has definitely not linear ?
There are four types of linear phase FIR filters, as described in this answer. They have to satisfy the following symmetry conditions:

$$h[n]=h[N-1-n]\quad \text{or}\quad h[n]=-h[N-1-n]\tag{1}$$

(assuming the impulse response $h[n]$ is zero for $n&lt;0$ and $n\ge N$). Since your filter satisfies neither of the two conditions given by $(1)$ it can't have a linear phase response.