Fuente TeX:

\displaystyle \left| \frac{n}{\sqrt{n^2+1}} - 1\right| = 1-\frac{n}{\sqrt{n^2+1}}= \frac{\sqrt{n^2+1}-n}{\sqrt{n^2+1}}= \frac{\left(\sqrt{n^2+1}-n\right)\left(\sqrt{n^2+1}+n\right)}{\sqrt{n^2+1}\left(\sqrt{n^2+1}+n\right)}=\frac{1}{\sqrt{n^2+1}(\sqrt{n^2+1}+n)}