Answer
Converges to $1$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (\dfrac{3}{n})^{1/n}$
Since, $\lim\limits_{n \to \infty} \sqrt[n] {n}=1$ and $\lim\limits_{n \to \infty} x^{1/n}=1$ when $x \gt 0$
So, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{3}{n})^{1/n}=\dfrac{\lim\limits_{n \to \infty} (3)^{1/n}}{\lim\limits_{n \to \infty} (n)^{1/n}}=\dfrac{1}{1}=1$
Hence, $\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} is convergent and converges to $1$
