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### Let \(x_n := -\frac{2}{n^2}\). Prove that \((x_n) \rightarrow 0\).

*Proof:* Given \(\varepsilon >0\),
let \(K > \sqrt{\tfrac{2}{\varepsilon}}\). Then if
\(n \ge K\) we have
\(|x_n - 0| = \)
\(\left|-\frac{2}{n^2}\right|=\)
\(\frac{2}{n^2}\le \)
\(\frac{2}{K^2}<\)
\(\frac{2}{(\sqrt{2/\varepsilon})^2}=\)
\(\varepsilon\).
Thus \(\left( -\frac{2}{n^2}\right)\rightarrow 0\) by the Definition of Sequence Converence.

Move on to Example 3