# Definition:Convergent Series/Normed Vector Space/Definition 2

Let $\struct {V, \norm {\, \cdot \,}}$ be a normed vector space.
Let $\displaystyle S := \sum_{n \mathop = 1}^\infty a_n$ be a series in $V$.
$S$ is convergent if and only if its sequence $\sequence {s_N}$ of partial sums converges in the normed vector space $\struct {V, \norm {\, \cdot \,}}$.