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Mathematics
Problem
Determine whether the series
∑
n
=
1
∞
sin
(
n
π
2
)
n
\displaystyle \sum_{n=1}^{\infty} \frac{\sin\left(\tfrac{n\pi}{2}\right)}{n}
n
=
1
∑
∞
n
sin
(
2
nπ
)
converges absolutely, converges conditionally, or diverges. Give a brief justification.
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