 Let us take an example. Suppose we take this tiger once again to raise the power of n un. Of course we need r to be greater than 2. So the DTFT cannot be evaluated if DTFT does not exist because r equal to 1 not allowed. But of course we can always take another example h n is half raised to the power of n un. And indeed in this case r needs to be greater than half. So r equal to 1 is allowed and therefore the DTFT exists. In fact capital H of z which is summation n going from 0 to infinity half raised to the power of n z raised to the power minus n which is the z transform of h n can be evaluated for r equal to 1. So this is the z transform and this can be evaluated. In general of course h z here happens to be 1 plus half z inverse plus half square z to the power minus 2 and so on. It is a geometric progression with common ratio half z inverse and therefore the sum is of course easy to evaluate. Now you know obviously the GP converges if mod half z inverse is less than 1 which means mod z is greater than half or it is the same thing as saying r is greater than half. Mod z is equal to r by definition. So we have mod z is equal to r. So we need r to be greater than half. And of course this h z can be written as 1 by 1 minus half z inverse mod z greater than half. Notice a z transform always has an expression and a region of convergence. A z transform is incomplete without any of these two. I shall shortly illustrate that if we did not specify the region of convergence here there would be an ambiguity in the sequence.