2.8.11 Power series

Problem: Find the radius of convergence of the given power series and the sum of this series, using theorems on differentiation and integration of series. First include the radius of convergence, and then the sum of the series or the value of the sum at the specified point. \[ \sum_{n=1}^{\infty} n x^{3 n-1}, \quad x_{0}=\frac{1}{2} . \]