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Putnam
1977 Putnam
B5
B5
Part of
1977 Putnam
Problems
(1)
Putnam 1977 B5
Source:
4/7/2022
Suppose that
a
1
,
a
2
,
…
a
n
a_1,a_2,\dots a_n
a
1
,
a
2
,
…
a
n
are real
(
n
>
1
)
(n>1)
(
n
>
1
)
and
A
+
∑
i
=
1
n
a
i
2
<
1
n
−
1
(
∑
i
=
1
n
a
i
)
2
.
A+ \sum_{i=1}^{n} a^2_i< \frac{1}{n-1} (\sum_{i=1}^{n} a_i)^2.
A
+
i
=
1
∑
n
a
i
2
<
n
−
1
1
(
i
=
1
∑
n
a
i
)
2
.
Prove that
A
<
2
a
i
a
j
A<2a_ia_j
A
<
2
a
i
a
j
for
1
≤
i
<
j
≤
n
.
1\leq i<j\leq n.
1
≤
i
<
j
≤
n
.
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