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Miklós Schweitzer
1968 Miklós Schweitzer
2
Miklos Schweitzer 1968_2
Miklos Schweitzer 1968_2
Source:
October 8, 2008
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inequalities
real analysis
real analysis unsolved
Problem Statement
Let
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
be nonnegative real numbers. Prove that
(
∑
i
=
1
n
a
i
)
(
∑
i
=
1
n
a
i
n
−
1
)
≤
n
∏
i
=
1
n
a
i
+
(
n
−
1
)
(
∑
i
=
1
n
a
i
n
)
.
( \sum_{i=1}^na_i)( \sum_{i=1}^na_i^{n-1}) \leq n \prod_{i=1}^na_i+ (n-1) ( \sum_{i=1}^na_i^n).
(
i
=
1
∑
n
a
i
)
(
i
=
1
∑
n
a
i
n
−
1
)
≤
n
i
=
1
∏
n
a
i
+
(
n
−
1
)
(
i
=
1
∑
n
a
i
n
)
.
J. Suranyi
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