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Canadian Junior Mathematical Olympiad
2024 Canadian Junior Mathematical Olympiad
2
Triple summation of fractions
Triple summation of fractions
Source: Canada Junior MO 2024/2
March 8, 2024
Problem Statement
Let
I
n
=
∑
i
=
1
n
∑
j
=
1
n
∑
k
=
1
n
min
(
1
i
,
1
j
,
1
k
)
I_n=\sum_{i=1}^n\sum_{j=1}^n\sum_{k=1}^n \min \left( \frac{1}{i}, \frac{1}{j}, \frac{1}{k} \right)
I
n
=
∑
i
=
1
n
∑
j
=
1
n
∑
k
=
1
n
min
(
i
1
,
j
1
,
k
1
)
and let
H
n
=
1
+
1
2
+
…
1
n
H_n=1+\frac{1}{2}+\ldots \frac{1}{n}
H
n
=
1
+
2
1
+
…
n
1
Find
I
n
−
H
n
I_n-H_n
I
n
−
H
n
in terms of
n
n
n
(Paraphrased)
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