Answer
Diverges
Work Step by Step
Let $u_n=\dfrac{\ln (n+1)}{(n+1)}$
When the numerator increases, the value of fraction is always increasing whereas when the denominator decreases, the value of the fraction is also increasing.
$\implies \dfrac{\ln (n+1)}{(n+1)} \gt \dfrac{1}{(n+1)}=(\dfrac{1}{n})$
Here, $\Sigma_{n=1}^\infty \dfrac{1}{n}$ is a divergent p-series test with $p=1$.
Thus, the series diverges by the limit comparison test.
