Answer
Absolutely Convergent
Work Step by Step
A series $ \Sigma a_n$ is said to be absolutely convergent when $ \Sigma |a_n|$ is convergent.
We notice that $ \Sigma_{n=1}^{\infty} |(-5)^{-n}|= \Sigma_{n=1}^{\infty} 5^{-n}$
We have a geometric series with common ratio $r=\dfrac{1}{5}$. When the common ratio $|r| \lt 1$, then a geometric series is convergent .
Therefore, the given series is Absolutely Convergent.
