Series

Last updated Nov 1, 2022

Let $(G, d)$ be a Metric Space so that $(G, +)$ is an Abelian Group. Suppose $({x}{n}){n=1}^{\infty} \subset {G}$. Denote the partial sums $p_{n} := \sum\limits_{i=1}^{n} x_{i}$. Then the Sequence $({p}{n}){n=1}^{\infty} \subset {G}$ is a Series. It is denoted $\sum\limits_{n=1}^{\infty} x_{n}$.