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1990 IMO Longlists
9
n variables inequality - ILL 1990 YUG4
n variables inequality - ILL 1990 YUG4
Source:
September 19, 2010
inequalities
inequalities proposed
Problem Statement
Let
{
a
1
,
a
2
,
…
,
a
n
}
=
{
1
,
2
,
…
,
n
}
\{ a_1, a_2, \ldots, a_n\} = \{1, 2, \ldots, n\}
{
a
1
,
a
2
,
…
,
a
n
}
=
{
1
,
2
,
…
,
n
}
. Prove that
1
2
+
2
3
+
⋯
+
n
−
1
n
≤
a
1
a
2
+
a
2
a
3
+
⋯
+
a
n
−
1
a
n
.
\frac 12 +\frac 23 +\cdots+\frac{n-1}{n} \leq \frac{a_1}{a_2} + \frac{a_2}{a_3} +\cdots+\frac{a_{n-1}}{a_n}.
2
1
+
3
2
+
⋯
+
n
n
−
1
≤
a
2
a
1
+
a
3
a
2
+
⋯
+
a
n
a
n
−
1
.
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