Question

Cho 6 số nguyên dương thỏa mãn: a<b<c<d<m<n

Chứng minh rằng : a+b/a+b+c+d+m+n < 1/3

Answer 1

ta có 

a<b<c=>3a<a+b+c

d<m<n=>3d<d+m+n

=>3a+3d<a+b+c+d+m+n

=>3a+3a/a+b+c+d+m+n<a+b+c+m+n+d/a+b+c+d+m+n

=>3(a+d)/a+b+c+d+m+n)<1

=>a+d/a+b+c+d+m+n<1/3  (đpcm)

copy

Answer 2

a<b<c<d<m<n =>a+b+c+d+m+n>a+b+a+b+a+b=3(a+b)

\(\Rightarrow\frac{a+b}{a+b+c+d+m+n}