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Undergraduate contests
IMC
2019 IMC
1
1
Part of
2019 IMC
Problems
(1)
(n^3+3n)^2/(n^6-64)
Source: IMC 2019 Day 1 P1
7/31/2019
Evaluate the product
∏
n
=
3
∞
(
n
3
+
3
n
)
2
n
6
−
64
.
\prod_{n=3}^{\infty} \frac{(n^3+3n)^2}{n^6-64}.
n
=
3
∏
∞
n
6
−
64
(
n
3
+
3
n
)
2
.
Proposed by Orif Ibrogimov, ETH Zurich and National University of Uzbekistan and Karen Keryan, Yerevan State University and American University of Armenia, Yerevan
college contests