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All-Russian Olympiad
1962 All Russian Mathematical Olympiad
025
ASU 025 All Russian MO 1962 10.4 a_{k-1}-2a_k+a_{k+1} >=0
ASU 025 All Russian MO 1962 10.4 a_{k-1}-2a_k+a_{k+1} >=0
Source:
June 17, 2019
algebra
Problem Statement
Given
a
0
,
a
1
,
.
.
.
,
a
n
a_0, a_1, ... , a_n
a
0
,
a
1
,
...
,
a
n
. It is known that
a
0
=
a
n
=
0
,
a
k
−
1
−
2
a
k
+
a
k
+
1
≥
0
a_0=a_n=0, a_{k-1}-2a_k+a_{k+1}\ge 0
a
0
=
a
n
=
0
,
a
k
−
1
−
2
a
k
+
a
k
+
1
≥
0
for all
k
=
1
,
2
,
.
.
.
,
k
−
1
k = 1, 2, ... , k-1
k
=
1
,
2
,
...
,
k
−
1
.Prove that all the numbers are nonnegative.
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