Answer
converges to $1$
Work Step by Step
As we know that when $x \gt 0$ so, $\lim\limits_{n \to \infty} \sqrt[n] {n}=1$ and $\lim\limits_{n \to \infty} x^{1/n}=1$
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (\dfrac{3}{n})^{1/n}$
This implies that $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{3}{n})^{1/n}$
and $a_n=\dfrac{\lim\limits_{n \to \infty} 3^{(1/n)}}{\lim\limits_{n \to \infty} n^{(1/n)}}=\dfrac{1}{1}=1$
Thus, $\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} converges to $1$