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Problems
Contests
National and Regional Contests
Moldova Contests
Chisinau City MO
1979 Chisinau City MO
170
170
Part of
1979 Chisinau City MO
Problems
(1)
Chisinau MO p170 1979 VIII a_{k-1}+ a_{k+1}<=2a_k
Source:
3/17/2021
The numbers
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
(
n
≥
3
n\ge 3
n
≥
3
) satisfy the relations
a
1
=
a
n
=
0
,
a
k
−
1
+
a
k
+
1
≤
2
a
k
(
k
=
2
,
3
,
.
.
.
,
n
−
1
)
a_1=a_n = 0, a_{k-1}+ a_{k+1}\le 2a_k \,\,\, (k = 2, 3,..., n-1)
a
1
=
a
n
=
0
,
a
k
−
1
+
a
k
+
1
≤
2
a
k
(
k
=
2
,
3
,
...
,
n
−
1
)
Prove that the numbers
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
are non-negative.
algebra
inequalities
recurrence relation