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China Team Selection Test
2018 China Team Selection Test
3
2018 China TST 3 Day 1 Q3
2018 China TST 3 Day 1 Q3
Source: Mar 20, 2018
March 27, 2018
inequalities
algebra
China TST
Problem Statement
Prove that there exists a constant
C
>
0
C>0
C
>
0
such that
H
(
a
1
)
+
H
(
a
2
)
+
⋯
+
H
(
a
m
)
≤
C
∑
i
=
1
m
i
a
i
H(a_1)+H(a_2)+\cdots+H(a_m)\leq C\sqrt{\sum_{i=1}^{m}i a_i}
H
(
a
1
)
+
H
(
a
2
)
+
⋯
+
H
(
a
m
)
≤
C
i
=
1
∑
m
i
a
i
holds for arbitrary positive integer
m
m
m
and any
m
m
m
positive integer
a
1
,
a
2
,
⋯
,
a
m
a_1,a_2,\cdots,a_m
a
1
,
a
2
,
⋯
,
a
m
, where
H
(
n
)
=
∑
k
=
1
n
1
k
.
H(n)=\sum_{k=1}^{n}\frac{1}{k}.
H
(
n
)
=
k
=
1
∑
n
k
1
.
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