Answer
Yes
Work Step by Step
The answer is YES.
Because, we have $\frac{1}{2}\Sigma_{n=1}^\infty a_n= \Sigma_{n=1}^\infty\dfrac{a_n}{2}$ also diverges and $\dfrac{a_n}{2} \lt a_n$
If we take a divergent series and divide each term by 2, we will still get a divergent series with smaller terms.
Hence, the answer is YES.
