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Mathematics
Problem
Decide whether the series
∑
n
=
1
∞
n
!
(
n
+
2
)
!
\displaystyle \sum_{n=1}^{\infty} \frac{n!}{(n+2)!}
n
=
1
∑
∞
(
n
+
2
)!
n
!
converges or diverges. Provide your conclusion and the
p
p
p
-value of the comparable
p
p
p
-series.
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