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Vojtěch Jarník IMC
1999 VJIMC
Problem 1
infinite product of k/(k+∞)
infinite product of k/(k+∞)
Source: VJIMC 1999 1.1
July 28, 2021
limits
real analysis
Problem Statement
Find the limit
lim
n
→
∞
(
∏
k
=
1
n
k
k
+
n
)
e
1999
n
−
1
.
\lim_{n\to\infty}\left(\prod_{k=1}^n\frac k{k+n}\right)^{e^{\frac{1999}n}-1}.
n
→
∞
lim
(
k
=
1
∏
n
k
+
n
k
)
e
n
1999
−
1
.
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