partial sum

**analysis** (differential/integral calculus, functional analysis, topology)

metric space, normed vector space

open ball, open subset, neighbourhood

convergence, limit of a sequence

compactness, sequential compactness

continuous metric space valued function on compact metric space is uniformly continuous

…

…

$\underoverset
{k = 0}
{\color{blue}\infty}
{\sum}
a_k$

its $n$th *partial sum* (for $n \in \mathbb{N}$ any natural number) is the actual sum

$\underoverset
{k = 0}
{\color{blue}n}
{\sum}
a_k$

of the first $n+1$ summands.

See also:

- Wikipedia,
*Partial sum*