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2
Prove that the product is not less than 2^n
Prove that the product is not less than 2^n
Source:
September 24, 2010
inequalities
algebra
IMO Longlist
IMO Shortlist
Problem Statement
Given
n
n
n
positive real numbers
a
1
,
a
2
,
…
,
a
n
a_1, a_2, \ldots , a_n
a
1
,
a
2
,
…
,
a
n
such that
a
1
a
2
⋯
a
n
=
1
a_1a_2 \cdots a_n = 1
a
1
a
2
⋯
a
n
=
1
, prove that
(
1
+
a
1
)
(
1
+
a
2
)
⋯
(
1
+
a
n
)
≥
2
n
.
(1 + a_1)(1 + a_2) \cdots (1 + a_n) \geq 2^n.
(
1
+
a
1
)
(
1
+
a
2
)
⋯
(
1
+
a
n
)
≥
2
n
.
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