Answer
Divergent
Work Step by Step
As we know that when $x \gt 0$, $\lim\limits_{n \to \infty}e^n=\infty$ and $e^{\ln x}=x$
Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \sinh (\ln n) $
This implies that $\lim\limits_{n \to \infty} \sinh (\ln n)=\lim\limits_{n \to \infty} \dfrac{e^{\ln n}-e^{(-\ln n)}}{2}$
and $\lim\limits_{n \to \infty} \dfrac{(n-\dfrac{1}{n})}{2}=\infty$
Thus, $\lim\limits_{n \to \infty} a_n=\infty$ and {$a_n$} is Divergent.