Evaluate the series ∑n=1∞arctan(1n2+n+1)\sum_{n=1}^{\infty} \arctan\left(\frac{1}{n^2+n+1}\right)∑n=1∞arctan(n2+n+11)
The series diverges
Converges to π4\frac{\pi}{4}4π
Converges to π6\frac{\pi}{6}6π
Converges to 111