Prove that following sequence is bounded I have to prove that $x_n=\frac{1-n}{\sqrt{2+n^2}}$ sequence is bounded. I've solved some easier ones, but these seems to be kinda different. I have to find actual bounds of the sequence.

Lower bound:
$$ \frac{1-n}{\sqrt{2+n^2}} = \frac{1}{\sqrt{2+n^2}} - \frac{n}{\sqrt{2+n^2}} \geq \frac{1}{\sqrt{2+n^2}} - \frac{n}{\sqrt{n^2}} = \frac{1}{\sqrt{2+n^2}} - 1 > -1$$
Upper bound:
Since $\sqrt{2+n^2} > 0$ we get
$$\frac{1-n}{\sqrt{2+n^2}} \leq \frac{1}{\sqrt{2+n^2}} < \frac{1}{\sqrt{2}}$$
