## Thomas' Calculus 13th Edition

Let us apply the Ratio Test to the given series. $\lim\limits_{n \to \infty} |\dfrac{u_{n+1}}{u_n}|=\lim\limits_{n \to \infty} \dfrac{e^n-e^{-n}}{e^{n+1}-e^{-n-1}}\\=\lim\limits_{n \to \infty} \dfrac{1-0}{e -0} \\=\dfrac{1}{e} \lt 1$ This implies that the series is Absolutely Convergent by the ratio test.