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Inequality holds for all real b ≥ 0 -IMO Long List P1
Inequality holds for all real b ≥ 0 -IMO Long List P1
Source:
August 28, 2010
inequalities
inequalities proposed
Problem Statement
Let
k
k
k
be one of the integers
2
,
3
,
4
2, 3,4
2
,
3
,
4
and let
n
=
2
k
−
1
n = 2^k -1
n
=
2
k
−
1
. Prove the inequality
1
+
b
k
+
b
2
k
+
⋯
+
b
n
k
≥
(
1
+
b
n
)
k
1+ b^k + b^{2k} + \cdots+ b^{nk} \geq (1 + b^n)^k
1
+
b
k
+
b
2
k
+
⋯
+
b
nk
≥
(
1
+
b
n
)
k
for all real
b
≥
0.
b \geq 0.
b
≥
0.
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