List of top Mathematics Questions on Power Series asked in IIT JAM MA

The radius of convergence of the series \( \displaystyle \sum_{n=1}^{\infty} \frac{(n!)^4}{(2n)!}(\log_e n)^{-1}x^n \) is rounded off to one decimal place.

For \( -1<x<1 \), the sum of the power series \[ 1 + \sum_{n=2}^{\infty} (-1)^{n-1} n^2 x^{n-1} \text{ is} \]

Let \( \{a_n\}_{n=0}^{\infty} \) and \( \{b_n\}_{n=0}^{\infty} \) be sequences of positive real numbers such that \( n a_n<b_n<n^2 a_n \), for all \( n \geq 2 \). If the radius of convergence of the power series \[ \sum_{n=0}^{\infty} a_n x^n \] is 4, then the power series \[ \sum_{n=0}^{\infty} b_n x^n \] is

The radius of convergence of the power series \[ \sum_{n=0}^{\infty} n! x^{n^2} \] is ...........

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