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Poland Contests
Polish MO Finals
1974 Polish MO Finals
4
4
Part of
1974 Polish MO Finals
Problems
(1)
Inequalities
Source: Poland 1973-1974
6/16/2016
Prove that, so have
k
k
k
for
∀
a
1
,
a
2
,
.
.
.
,
a
n
\forall a_1,a_2,...,a_n
∀
a
1
,
a
2
,
...
,
a
n
satisfying
∣
∑
i
=
1
k
a
i
−
∑
j
=
k
+
1
n
a
j
∣
≤
max
1
≤
m
≤
n
∣
a
m
∣
|\sum_{i=1}^k a_i -\sum_{j=k+1}^n a_j |\leq \max_{1\leq m\leq n} |a_m|
∣
i
=
1
∑
k
a
i
−
j
=
k
+
1
∑
n
a
j
∣
≤
1
≤
m
≤
n
max
∣
a
m
∣
inequalities