Answer
Absolutely Convergent
Work Step by Step
We need to apply the Ratio Test to the series.
$\lim\limits_{n \to \infty} |\dfrac{u_{n+1}}{u_n}|=\lim\limits_{n \to \infty} |\dfrac{n+2}{4n+2}|$
or, $=\lim\limits_{n \to \infty} \dfrac{n/n+2/n}{4n/n+2/n}$
or, $=\lim\limits_{n \to \infty} \dfrac{1+2/n}{4+2/n}$
So, $=\dfrac{1}{4} \lt 1$
Thus, the series is Absolutely Convergent by the ratio test.
