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Saint Petersburg Mathematical Olympiad
2013 Saint Petersburg Mathematical Olympiad
5
St.Peterburg, P5 Grade 11, 2013
St.Peterburg, P5 Grade 11, 2013
Source:
April 17, 2014
inequalities
induction
inequalities proposed
Problem Statement
Let
x
1
x_1
x
1
, ... ,
x
n
+
1
∈
[
0
,
1
]
x_{n+1} \in [0,1]
x
n
+
1
∈
[
0
,
1
]
and
x
1
=
x
n
+
1
x_1=x_{n+1}
x
1
=
x
n
+
1
. Prove that
∏
i
=
1
n
(
1
−
x
i
x
i
+
1
+
x
i
2
)
≥
1.
\prod_{i=1}^{n} (1-x_ix_{i+1}+x_i^2)\ge 1.
i
=
1
∏
n
(
1
−
x
i
x
i
+
1
+
x
i
2
)
≥
1.
A. Khrabrov, F. Petrov
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