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Mathematics
Problem
Decide whether the series
∑
n
=
1
∞
(
n
!
)
1
/
n
n
3
/
2
\displaystyle \sum_{n=1}^{\infty} \frac{(n!)^{1/n}}{n^{3/2}}
n
=
1
∑
∞
n
3/2
(
n
!
)
1/
n
converges or diverges. Provide your conclusion only.
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