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Let ${x_n}$ be the sequence $+\sqrt{1}, -\sqrt{1},+\sqrt{2}, -\sqrt{2},+\sqrt{3}, -\sqrt{3}$ ...

If

$$y_n = \frac{{x_1}+{x_2}+...+{x_n}}{n}$$ for all $n \in\Bbb N$, then the sequence $\{y_n\}$ is:

a) Monotonic or b) Not Bounded or c) Bounded but not Convergent or d) Convergent.

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    Calculate $y_1$, $y_2$, $y_3$, $y_4$, $y_5$, $y_6$. (No calculaor, just observe the obvious cancellations.) I think the answers will become clear.2012-08-14
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    This question was in my exam. Now,I can try to solve it ...thanks2012-08-14
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    Well clearly a) is not the answer, since if the sequence is monotonic then it is either not bounded or convergent.2012-08-14

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