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Tutorial Exercise
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.
$\sum_{n=1}^{\infty} \frac{(-1)^n \arctan(n)}{n^{13}}$
Step 1
We know that the arctangent function has lower and upper limits $-\frac{\pi}{2} < \arctan(x) < \frac{\pi}{2}$
Step 2
Therefore $|\frac{(-1)^n \arctan(n)}{n^{13}}| < \frac{\arctan(n)}{n^{13}}$
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