Why does x(n) converge in one case and diverge in the other?

[fireflies]

I actually don't know what math sub-topic it belong to..

To the question, I got this two in my class assignment. Why x(n) is different can anybody tell me? What is the difference in these two questions (except that the one has 10 included and other not. Is the difference for that?)??

 

[FactChecker]

The values of x in the table are different.

 

[fireflies]

yes, but that's the solution. My question is there is no difference in question, so why in solutions?

 

[FactChecker]

Usually when they say "Let x(z)=...", they go on to say things about x. It may not be the final solution, but it may be used to find the solution. The two solutions may start with different x's and do something different to each to derive the same final answer. Are you sure that there is not more in those solutions than the first parts you are showing?