MathCastle
ChallengeMediumTelescoping & Recursion

Telescoping & Recursion · Medium problem

Evaluate ∑n=1∞arctan⁡ ⁣(1n2+n+1)\displaystyle\sum_{n=1}^{\infty}\arctan\!\left(\dfrac{1}{n^{2}+n+1}\right).