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2024-IMOC
A1
Infinite Series with Fraction
Infinite Series with Fraction
Source: 2024 imocsl A1 (Night 2-A)
August 8, 2024
algebra
IMOC
inequalities
series
Problem Statement
Given a positive integer
N
N
N
. Prove that
∑
m
=
1
N
∑
n
=
1
N
1
m
n
2
+
m
2
n
+
2
m
n
<
7
4
.
\sum_{m=1}^N \sum_{n=1}^N \frac{1}{mn^2+m^2n+2mn}<\frac{7}{4}.
m
=
1
∑
N
n
=
1
∑
N
m
n
2
+
m
2
n
+
2
mn
1
<
4
7
.
Proposed by tan-1
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