Determine the convergence of the series ∑n=1∞(π2−arctan(n2))\sum_{n=1}^{\infty} \left( \frac{\pi}{2} - \arctan(n^2) \right)∑n=1∞(2π−arctan(n2)).
Converges by the Comparison Test with ∑1n2\sum \frac{1}{n^2}∑n21
Converges by the Ratio Test
Diverges because the limit of the terms is not zero
Diverges by the Integral Test