[tex]a=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+_{\dots}+\frac{1}{2011}\\
\\
b=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+_{\dots}+\frac{2010}{2011}\\
\\
m_a=\frac{a+b}{2}\\
m_a=\dfrac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+_{\dots}+\frac{1}{2011}+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+_{\dots}+\frac{2010}{2011}}{2}\\
m_a=\dfrac{\left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{1}{3}+\frac{2}{3}\right)+_{\dots}+\left(\frac{1}{2011}+\frac{2010}{2011}\right)}{2}\\
~~~~~~~~~~~De\ 2010\ ori\\
m_a=\frac{\overbrace{1+1+_{\dots}+ 1}}{2}[/tex]
[tex]m_a=\frac{2010}{2}=\boxed{1005}[/tex]
