Answer
Divergent
Work Step by Step
Consider $\lim\limits_{n \to \infty} n \tan (\dfrac{1}{n})=\lim\limits_{n \to \infty} \dfrac{\tan (\dfrac{1}{n})}{(\dfrac{1}{n})})$
and $\lim\limits_{x \to 0} \dfrac{\tan x}{x}= 1 \ne 0$
As per the n-th term Test of Divergence, the series is Divergent.