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Mathematics
Problem
Determine whether the series
∑
n
=
1
∞
(
−
1
)
n
−
1
n
!
n
n
\displaystyle\sum_{n=1}^{\infty} (-1)^{n-1}\,\dfrac{n!}{n^{n}}
n
=
1
∑
∞
(
−
1
)
n
−
1
n
n
n
!
converges absolutely, converges conditionally, or diverges. State your conclusion.
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