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All-Russian Olympiad
1969 All Soviet Union Mathematical Olympiad
128
ASU 128 All Soviet Union MO 1969 ... +a_n/(a_1+a_2)> n/4
ASU 128 All Soviet Union MO 1969 ... +a_n/(a_1+a_2)> n/4
Source:
June 23, 2019
algebra
inequalities
Problem Statement
Prove that for the arbitrary positive
a
1
,
a
2
,
.
.
.
,
a
n
a_1, a_2, ... , a_n
a
1
,
a
2
,
...
,
a
n
the following inequality is held
a
1
a
2
+
a
3
+
a
2
a
3
+
a
4
+
.
.
.
.
+
a
n
−
1
a
n
+
a
1
+
a
n
a
1
+
a
2
>
n
4
\frac{a_1}{a_2+a_3}+\frac{a_2}{a_3+a_4}+....+\frac{a_{n-1}}{a_n+a_1}+\frac{a_n}{a_1+a_2}>\frac{n}{4}
a
2
+
a
3
a
1
+
a
3
+
a
4
a
2
+
....
+
a
n
+
a
1
a
n
−
1
+
a
1
+
a
2
a
n
>
4
n
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