List of top Complex Analysis Questions on Radius of convergence asked in GATE MA

For \(a_n \in \mathbb{C}\), \(n = 0,1,2,\ldots\), the power series \[ \sum_{n=0}^{\infty} a_n (z-2)^n \] converges at \(z = 5\) and diverges at \(z = -1\). Then the radius of convergence of this power series is equal to ______. (Answer in integer)

The radius of convergence of the series \[ \sum_{n \geq 0} 3^{n+1} z^{2n}, \quad z \in \mathbb{C} \] is __________ (round off to TWO decimal places).