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What is the interval of convergence of the power series:

$$\sum_{n=1}^\infty \frac{(-4)^n}{n} x^{2n}$$

A

$\left(-\cfrac{1}{2},\cfrac{1}{2}\right)$

B

$\left(-\cfrac{1}{2},\cfrac{1}{2}\right]$

C

$\left[-\cfrac{1}{2},\cfrac{1}{2}\right)$

D

$\left[-\cfrac{1}{2},\cfrac{1}{2}\right]$

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