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International Contests
Tournament Of Towns
1994 Tournament Of Towns
(438) 4
(438) 4
Part of
1994 Tournament Of Towns
Problems
(1)
prod (1+a_k^2 / a_{k+1}) > = prod (1+a_k)
Source: TOT 438 1994 Autumn A S4 - Tournament of Towns
6/12/2024
Prove that for all positive
a
1
.
a
2
,
.
.
.
,
a
n
a_1. a_2, ..., a_n
a
1
.
a
2
,
...
,
a
n
the inequality
(
1
+
a
1
2
a
2
)
(
1
+
a
2
2
a
3
)
.
.
.
(
1
+
a
n
2
a
1
)
≥
(
1
+
a
1
)
(
1
+
a
2
)
.
.
.
(
1
+
a
n
)
\left( 1+\frac{a_1^2}{a_2}\right) \left( 1+\frac{a_2^2}{a_3}\right) ...\left( 1+\frac{a_n^2}{a_1}\right) \ge (1+a_1)(1+a_2)...(1+a_n)
(
1
+
a
2
a
1
2
)
(
1
+
a
3
a
2
2
)
...
(
1
+
a
1
a
n
2
)
≥
(
1
+
a
1
)
(
1
+
a
2
)
...
(
1
+
a
n
)
holds. (LD Kurliandchik)
algebra
inequalities