## Thomas' Calculus 13th Edition

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.