Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent, enter div. \[ \sum_{n=1}^{\infty} \arctan (17 n) \] Answer:
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To determine whether the series \(\sum_{n=1}^{\infty} \arctan(17n)\) is convergent or divergent, we can analyze the behavior of the terms as \(n\) approaches infinity. The term \(\arctan(17n)\) approaches \(\frac{\pi}{2}\) as \(n\) grows larger since the arctangent function asymptotically approaches \(\frac{\pi}{2}\). This means that the terms of our series do not approach zero: \[ \lim_{n \to \infty} \arctan(17n) = \frac{\pi}{2} \neq 0. \] Since the terms do not tend to zero, the series \(\sum_{n=1}^{\infty} \arctan(17n)\) diverges. Therefore, the answer is: div
