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1990 Irish Math Olympiad
4
2^k Inequality
2^k Inequality
Source: 1990 IrMO Paper 1 Problem 4
September 30, 2017
inequalities
Problem Statement
The real number
x
x
x
satisfies all the inequalities
2
k
<
x
k
+
x
k
+
1
<
2
k
+
1
2^k<x^k+x^{k+1}<2^{k+1}
2
k
<
x
k
+
x
k
+
1
<
2
k
+
1
for
k
=
1
,
2
,
…
,
n
k=1,2,\dots ,n
k
=
1
,
2
,
…
,
n
. What is the greatest possible value of
n
n
n
?
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