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Mathematics
Problem
Determine whether the series
∑
n
=
1
∞
(
−
1
)
n
−
1
n
n
2
+
1
\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1}\,\frac{n}{n^{2}+1}
n
=
1
∑
∞
(
−
1
)
n
−
1
n
2
+
1
n
converges absolutely, converges conditionally, or diverges. Give a brief justification.
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