Z-Transform Initial Value Theorem

Question

I have a small understanding of how to solve limits to infinity for regular rational equations, but I'm unsure of how to apply this to the Z-Transform initial value theorem.

The equation is: \$ \lim_{z \rightarrow \infty} \frac{10z^{-1}+5z^{-2}}{1-1.2z^{-1}+0.2z^{-2}} \$

The answer for this is that \$ x(n) = 0 \$, but I'm unsure of how to arrive at that.

I have watched this YouTube video which helps with understanding the general concept, but I'm not sure how to apply this to Z-Transforms.

Any help would be much appreciated.

Answer 1

$$\lim_{z\to\infty}z^{-1} = 0,$$

so your limit becomes

$$ \frac{0 + 0}{1 - 0 + 0},$$ or \$\frac{0}{1}.\$