Answer
Converges
Work Step by Step
Here, we have the given series $\Sigma_{n=1}^{\infty} \dfrac{\ln n}{n^2}$
Next, we will use the nth term test for the given series to check whether it is convergent or divergent.
By using L-hospital's rule: $\Sigma_{n=1}^{\infty} \dfrac{\ln n}{n^2}=\lim\limits_{n \to \infty} \dfrac{1}{2n^2}=0 \lt 1$
Hence, we can conclude that the given series converges by the nth term test .
