Answer by hamam_Abdallah for Inconclusive convergence tests and Divergence Test

You know that for a real or complex sequence $ ( u_n)$, we have the equivalence

$$\boxed{\lim_{n\to+\infty}u_n=0\iff \lim_{n\to+\infty}|u_n|=0}$$

So,

$$\lim_{n\to+\infty}|u_n|\ne 0\implies$$$$\lim_{n\to+\infty}u_n \ne 0 \implies$$$$\sum u_n \text{ is divergent}$$