Answer
$4$.
Work Step by Step
We need to apply ratio test for a given series.
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_n}|=\lim\limits_{n \to \infty} |\dfrac{1/2^{2(n+1)}}{1/2^{2n}}|=\dfrac{1}{4}$
This implies that the radius of convergence of the series is $4$ and the series converges at $(-4,4)$ but diverges at endpoints.
