## University Calculus: Early Transcendentals (3rd Edition)

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.