Understand the Difference Between Convergence and Divergence of x(n)

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The discussion centers around a math assignment involving two questions that appear similar but yield different solutions for the variable x(n). The main inquiry is why the solutions differ despite the questions seemingly being the same, aside from one including the number 10. Participants highlight that while the initial questions may appear identical, the differences in the values of x in the solutions suggest that there are underlying distinctions in the problem-solving approach. It is noted that when a function like x(z) is introduced, it often serves as a stepping stone to reach the final answer, implying that different starting points or methods can lead to the same conclusion. The conversation emphasizes the importance of examining the full context of the solutions to understand the discrepancies fully.
fireflies
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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?)??
 

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The values of x in the table are different.
 
yes, but that's the solution. My question is there is no difference in question, so why in solutions?
 
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?
 

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