## Thomas' Calculus 13th Edition

Let $a_n=\dfrac{2^n 3^n}{n^n}$ and $a_{n+1}=\dfrac{2^{n+1} 3^{n+1}}{n^{n+1}}$ The root Test states that $\lim\limits_{n \to \infty} \sqrt[n]{|a_n|}=\lim\limits_{n \to \infty} |a_n|^{1/n}$ Then $\lim\limits_{n \to \infty} \sqrt[n]{|\dfrac{2^{(n)} 3^{(n)}}{n^n}|}=\lim\limits_{n \to \infty} |\dfrac{2^{(n)} 3^{(n)}}{n^n}|^{1/n}$ Here, $\lim\limits_{n \to \infty} \dfrac{6}{n}=\dfrac{6}{\infty}=0 \lt 1$ Thus, the series Converges Absolutely by the Root Test.