MathDB
Problems
Contests
International Contests
Tournament Of Towns
1986 Tournament Of Towns
(118) 6
(118) 6
Part of
1986 Tournament Of Towns
Problems
(1)
TOT 118 1986 Spring S6 a^2_1-a^2_2+ ...+a^2_{2n- l} \ge (a_1- ...+a_{2n- l})^2
Source:
8/29/2019
Given the nonincreasing sequence of non-negative numbers in which
a
1
≥
a
2
≥
a
3
≥
.
.
.
≥
a
2
n
−
1
≥
0
a_1 \ge a_2 \ge a_3 \ge ... \ge a_{2n-1}\ge 0
a
1
≥
a
2
≥
a
3
≥
...
≥
a
2
n
−
1
≥
0
.Prove that
a
1
2
−
a
2
2
+
a
3
2
−
.
.
.
+
a
2
n
−
l
2
≥
(
a
1
−
a
2
+
a
3
−
.
.
.
+
a
2
n
−
l
)
2
a^2_1 -a^2_2 + a^2_3 - ... + a^2_{2n- l} \ge (a_1 - a_2 + a_3 - ... + a_{2n- l} )^2
a
1
2
−
a
2
2
+
a
3
2
−
...
+
a
2
n
−
l
2
≥
(
a
1
−
a
2
+
a
3
−
...
+
a
2
n
−
l
)
2
.( L . Kurlyandchik , Leningrad )
algebra
inequalities