Question

Cho 6 số nguyên dương 0< a < b < c < d < m < n. Chứng minh: a+c+m/a+b+c+d+m+n < 1/3

Answer 1

Sửa  đề c/m \(\frac{a+c+m}{a+b+c+d+m+n}< \frac{1}{2}\)

Ta có: \(\hept{\begin{cases}a< b\Rightarrow2a< a+b\\c< d\Rightarrow2c< c+d\\m< n\Rightarrow2m< m+n\end{cases}}\)

=>\(2\left(a+c+m\right)< a+b+c+d+m+n\)

=>\(\frac{a+c+m}{a+b+c+d+m+n}< \frac{1}{2}\)

Answer 2

Sửa đề: Chứng minh: \(\frac{a+c+m}{a+b+c+d+m+n}< \frac{1}{2}\)

Ta có: \(\hept{\begin{cases}a< b\Rightarrow2a< a+b\\c< d\Rightarrow2c< c+d\\m< n\Rightarrow2m< m+n\end{cases}}\)

\(\Rightarrow2\left(a+c+m\right)< a+b+c+d+m+n\)

\(\Rightarrow\frac{a+c+m}{a+b+c+d+m+n}< \frac{1}{2}\)