Evaluate the infinite sum S=∑n=1∞arctan(12n2)S = \sum_{n=1}^{\infty} \arctan\left(\frac{1}{2n^2}\right)S=∑n=1∞arctan(2n21).
π/4\pi/4π/4
π/2\pi/2π/2
π/3\pi/3π/3
π/6\pi/6π/6