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Determine the convergence of the series sin (log n)

Consider the series

    \[ \sum_{n=1}^{\infty} \sin (\log n). \]

Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.


The given series diverges since

    \[ \lim_{n \to \infty} \sin (\log n) \neq 0. \]

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