## Thomas' Calculus 13th Edition

Let us apply the Ratio Test to the given series. $\lim\limits_{n \to \infty} |\dfrac{u_{n+1}}{u_n}|=\lim\limits_{n \to \infty} |\dfrac{n+2}{4n+2}| \\=\lim\limits_{n \to \infty} \dfrac{1+2/n}{4+2/n} \\=\dfrac{1}{4} \lt 1$ This implies that the series Absolutely Converges by the ratio test.