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