# How do you use the Nth term test on the infinite series #sum_(n=1)^ooarctan(n)# ?

Since

by Divergence Test (Nth Term Test), we can conclude that

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To use the Nth term test for divergence on the series ( \sum_{n=1}^{\infty} \arctan(n) ), we evaluate the limit of the nth term as ( n ) approaches infinity. If this limit is not zero, then the series diverges.

For the given series, ( \arctan(n) ) does not approach zero as ( n ) approaches infinity (it oscillates between ( -\frac{\pi}{2} ) and ( \frac{\pi}{2} )), so the Nth term test is inconclusive.

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