Answer
Absolutely Convergent
Work Step by Step
We need to apply the Root Test to the series.
$L=\lim\limits_{n \to \infty} |a_n|^{1/n}=\lim\limits_{n \to \infty} |\dfrac{(-1)^n(n+1)^n}{(2n)^n}|=\Sigma_{n=1}^{\infty} \dfrac{n+1}{2n}$
or, $=\Sigma_{n=1}^{\infty} \dfrac{n/n+1/n}{2n/n}$
So, $=\dfrac{1}{2} \lt 1$
Thus, the series is Absolutely Convergent by the ratio test.