How can I find the inverse Z-transform of $1/z$?

Question

I'm trying to find the sequence ${a_n}$ given the Z-transform $A(z)=1/z$

I'm not sure though how to calculate the inverse transform of $A(z)$, All help is much appreciated

Answer 1

The Z-transform of a sequence $a_n$ is defined as $A(z)=\sum_{n=-\infty}^{\infty} a_n z^{-n}$.

In your case, $A(z)=1/z=z^{-1}$, so this must mean $a_n=0$ for all $n\neq 1$, and $a_1=1$. We don't need any fancy computations in this example, we just read off the one nonzero coefficient directly from $A$.