Answer
$\dfrac{1}{2}$
Work Step by Step
We need to apply ratio test for a given series.
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_n}|=\lim\limits_{n \to \infty} |\dfrac{2^{n+1}}{n+1} \times \dfrac{n}{2^n}|=2$
This implies that the radius of convergence of the series is $\dfrac{1}{2}$ and the series converges at $[-\dfrac{1}{2},\dfrac{1}{2})$ but diverges at endpoint $\dfrac{1}{2}$.
