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2011 Kosovo National Mathematical Olympiad
1
Compare x^y and y^x, [KMO #1. (Grade 9)]
Compare x^y and y^x, [KMO #1. (Grade 9)]
Source:
March 13, 2011
logarithms
Problem Statement
Let
x
=
(
1
+
1
n
)
n
x = \left( 1 + \frac{1}{n}\right)^n
x
=
(
1
+
n
1
)
n
and
y
=
(
1
+
1
n
)
n
+
1
y = \left( 1 + \frac{1}{n}\right)^{n+1}
y
=
(
1
+
n
1
)
n
+
1
where
n
∈
N
n \in \mathbb{N}
n
∈
N
. Which one of the numbers
x
y
x^y
x
y
,
y
x
y^x
y
x
is bigger ?
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