List of top Mathematics Questions on Convergence tests asked in IIT JAM MA

Which of the following is TRUE?

The sum of the series \[ \sum_{n=1}^{\infty} \tan^{-1} \left( \frac{2}{n^2} \right) \] is

The interval of convergence of the power series \[ \sum_{n=1}^{\infty} \frac{1}{(-3)^n + 2} \frac{(4x - 12)^n}{n^2 + 1} \] is