Answer
Diverges
Work Step by Step
We are given the series $\Sigma_{n=0}^{\infty} \dfrac{(-1)^n n}{\ln n}$
We will apply the nth test to check whether the given series converges or diverges.
So, we have
$\lim\limits_{n \to \infty} \dfrac{(-1)^n n}{\ln n}=\infty$
This means that the given series diverges.
