Question: Convergence conditions for series


I'm quite new to Maple and as practise, I want to calculate some z-Transformations via the definition (sum).

sum(z^(-k),k=0..infinity) assuming abs(z)>1; this one works fine (after I added the convergence condition abs(z)>1.

sum(exp(a*k*Ta)*z^(-k),k=0..infinity) assuming abs(exp(a*Ta)*z^(-1))>1; doesn't work. But I if I change the convergence condition to a*Ta<ln(z), it is calculated correctly. Why does the first attempt not work? What is the correct way to tell maple the convergence condition?

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