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Problems
Contests
National and Regional Contests
China Contests
China Team Selection Test
2005 China Team Selection Test
1
Sum of denominators
Sum of denominators
Source: China TST 2005
June 27, 2006
inequalities
algebra
Problem Statement
Prove that for any
n
n
n
(
n
≥
2
n \geq 2
n
≥
2
) pairwise distinct fractions in the interval
(
0
,
1
)
(0,1)
(
0
,
1
)
, the sum of their denominators is no less than
1
3
n
3
2
\frac{1}{3} n^{\frac{3}{2}}
3
1
n
2
3
.
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