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China National Olympiad
1993 China National Olympiad
2
2
Part of
1993 China National Olympiad
Problems
(1)
China Mathematical Olympiad 1993 problem2
Source: China Mathematical Olympiad 1993 problem2
9/22/2013
Given a natural number
k
k
k
and a real number
a
(
a
>
0
)
a (a>0)
a
(
a
>
0
)
, find the maximal value of
a
k
1
+
a
k
2
+
⋯
+
a
k
r
a^{k_1}+a^{k_2}+\cdots +a^{k_r}
a
k
1
+
a
k
2
+
⋯
+
a
k
r
, where
k
1
+
k
2
+
⋯
+
k
r
=
k
k_1+k_2+\cdots +k_r=k
k
1
+
k
2
+
⋯
+
k
r
=
k
(
k
i
∈
N
,
1
≤
r
≤
k
k_i\in \mathbb{N} ,1\le r \le k
k
i
∈
N
,
1
≤
r
≤
k
).
inequalities
inequalities unsolved