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International Contests
IMO Longlists
1987 IMO Longlists
14
n variables ILL 1987 inequality
n variables ILL 1987 inequality
Source:
September 5, 2010
inequalities
inequalities proposed
Problem Statement
Given
n
n
n
real numbers
0
<
t
1
≤
t
2
≤
⋯
≤
t
n
<
1
0 < t_1 \leq t_2 \leq \cdots \leq t_n < 1
0
<
t
1
≤
t
2
≤
⋯
≤
t
n
<
1
, prove that
(
1
−
t
n
2
)
(
t
1
(
1
−
t
1
2
)
2
+
t
2
(
1
−
t
2
3
)
2
+
⋯
+
t
n
(
1
−
t
n
n
+
1
)
2
)
<
1.
(1-t_n^2) \left( \frac{t_1}{(1-t_1^2)^2}+\frac{t_2}{(1-t_2^3)^2}+\cdots +\frac{t_n}{(1-t_n^{n+1})^2} \right) < 1.
(
1
−
t
n
2
)
(
(
1
−
t
1
2
)
2
t
1
+
(
1
−
t
2
3
)
2
t
2
+
⋯
+
(
1
−
t
n
n
+
1
)
2
t
n
)
<
1.
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