Determine the convergence of the series ∑n=1∞(π2−arctan(n))\sum_{n=1}^{\infty} \left( \frac{\pi}{2} - \arctan(n) \right)∑n=1∞(2π−arctan(n)).
Converges by the Limit Comparison Test with ∑1n\sum \frac{1}{n}∑n1.
Diverges by the Limit Comparison Test with ∑1n\sum \frac{1}{n}∑n1.
Converges by the Alternating Series Test.
Diverges by the Divergence Test.