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JBMO TST - Moldova
2019 Junior Balkan Team Selection Tests - Moldova
4
Moldova JTST 2019 P4
Moldova JTST 2019 P4
Source:
April 19, 2019
algebra
inequalities
Problem Statement
Let
n
(
n
≥
2
)
n(n\geq2)
n
(
n
≥
2
)
be a natural number and
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
natural positive real numbers. Determine the least possible value of the expression
E
n
=
(
1
+
a
1
)
⋅
(
a
1
+
a
2
)
⋅
(
a
2
+
a
3
)
⋅
.
.
.
⋅
(
a
n
−
1
+
a
n
)
⋅
(
a
n
+
3
n
+
1
)
a
1
⋅
a
2
⋅
a
3
⋅
.
.
.
⋅
a
n
E_n=\frac{(1+a_1)\cdot(a_1+a_2)\cdot(a_2+a_3)\cdot...\cdot(a_{n-1}+a_n)\cdot(a_n+3^{n+1})} {a_1\cdot a_2\cdot a_3\cdot...\cdot a_n}
E
n
=
a
1
⋅
a
2
⋅
a
3
⋅
...
⋅
a
n
(
1
+
a
1
)
⋅
(
a
1
+
a
2
)
⋅
(
a
2
+
a
3
)
⋅
...
⋅
(
a
n
−
1
+
a
n
)
⋅
(
a
n
+
3
n
+
1
)
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