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} |\dfrac{(-1)^{n-1}}{n^2+2n+1}|= \Sigma_{n=2}^{\infty} \dfrac{1}{n^2}$
Thus we have a p-series with common ratio $r=2$. When the common ratio $r \gt 1$, then a p-series is convergent.
Therefore, the given series is Absolutely Convergent.
