Question

a<b<c<d<m<n là các số nguyên.CMR:\(\frac{a+c+m}{a+b+c+d+m+n}< \frac{1}{2}\)

Answer 1

\(\dfrac{a+c+m}{a+b+c+d+m+n}< \dfrac{a+c+m}{a+c+m+a+c+m}\)

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

\(\Rightarrowđpcm\)

Answer 2

\(\dfrac{a+c+m}{a+b+c+d+m+n}< \dfrac{a+c+m}{a+b+c+a+b+c}\left(a< b< c< d< m< n\right)\)\(\Rightarrow\dfrac{a+c+m}{a+b+c+d+m+n}< \dfrac{a+c+m}{2a+2c+2m}\)

\(\Rightarrow\dfrac{a+c+m}{a+b+c+d+m+n}< \dfrac{a+c+m}{2\left(a+c+m\right)}\)

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