A series $\left\{a_n\right\}$ is said to be absolutely convergent if ${\sum }_{n=1}^{\infty }\left|a_n\right|$ is convergent. Absolutely convergent series are convergent. If $a_n={\left(-1\right)}^{n-1}\times \frac{1}{n}$ then the series is convergent but not absolutely convergent, whereas $a_n={\left(-1\right)}^{n-1}\times \frac{1}{n^2}$ is absolutely convergent. A series which is convergent but not absolutely convergent is called conditionally convergent.