#### Answer

Absolutely Convergent

#### Work Step by Step

A series $ \Sigma a_n$ is defined as the absolutely convergent when the series $ \Sigma |a_n|$ is convergent.
From the series, we notice that
$ \Sigma_{n=1}^{\infty} |\dfrac{(-1)^{n-1}}{n^2+2n+1}|= \Sigma_{n=2}^{\infty} \dfrac{1}{n^2}$
This suggests a $P-$ series with common ratio $r=2 \gt 1$
Remember that a p- series is said to be convergent when the common ratio $r \gt 1$.
This implies that the series is Absolutely Convergent.