summable series

Let $\{v_n\}$ be a seq of points in vector space $V$. The the series $\sum _n{v}_n$ is summable if ${\left\{\sum _{n=1}^m{v}_n\right\}}_{m=1}^{\mathrm{\infty }}$ converges.

The series is absolutely summable if ${\{\sum _{n=1}^m||v_n||\}}_{m=1}^{\mathrm{\infty }}$ converges.