Answer
Divergent
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \sinh (\ln n) $
Since, $e^{\ln x}=x$
So, $\lim\limits_{n \to \infty} \sinh (\ln n)=\lim\limits_{n \to \infty} \dfrac{e^{\ln n}-e^{-\ln n}}{2}=\lim\limits_{n \to \infty} \dfrac{n-1/n}{2}$
or, $=\infty$
Hence, $\lim\limits_{n \to \infty} a_n=\infty$ and {$a_n$} is Divergent
