[tex]\displaystyle\\
0,(3)+\left|-2,5+1\frac{1}{6}\right|=\\\\\\
=\frac{1}{3}+\left|-2,5+\frac{7}{6}\right|=\\\\\\
=\frac{1}{3}+\left|\frac{-5}{2}+\frac{7}{6}\right|=\\\\\\
=\frac{1}{3} + \left| \frac{-15}{6} + \frac{7}{6} \right| = \\ \\ \\
=\frac{1}{3} + \left| \frac{-15+7}{6} \right| = \\ \\ \\
=\frac{1}{3} + \left| \frac{-8}{6} \right| = \\ \\ \\
=\frac{1}{3} + \left| -\frac{4}{3} \right| = \\ \\ \\
=\frac{1}{3} +\frac{4}{3}= \boxed{\frac{5}{3} }[/tex]
