Ta có : \(a< b< c< d< m< n\Rightarrow a+b+c< d+m+n\)
\(\Leftrightarrow2a+2b+2c< a+b+c+d+m+n\)
\(\Leftrightarrow2\left(a+b+c\right)< a+b+c+d+m+n\)
\(\Rightarrow\frac{2\left(a+b+c\right)}{a+b+c+d+m+n}< \frac{a+b+c+d+m+n}{a+b+c+d+m+n}=1\)
\(\Rightarrow\frac{a+b+c}{a+b+c+d+m+n}< \frac{1}{2}\)(đpcm)