Answer
Divergent
Work Step by Step
Since, we have $\lim\limits_{n \to \infty} n \tan (\dfrac{1}{n})$
or, $\lim\limits_{n \to \infty} n \tan (\dfrac{1}{n})=\lim\limits_{n \to \infty} \dfrac{\tan (1/n)}{1/n})$
or, $=\lim\limits_{n \to \infty} \sec^2 (1/n)$
or, $ 1 \ne 0$
Hence, the series is Divergent by the n-th term Test for Divergence
