Answer
Converges
Work Step by Step
Given: $a_{n+1}=(\dfrac{2}{n})a_n$ and $a_1=2$
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{(\dfrac{2}{n})a_n}{a_n}|$
$\implies \lim\limits_{n \to \infty}|\dfrac{2}{n}|=\dfrac{2}{\infty}=0 \lt 1$
Thus, the series converges by the ratio test.