series

What you get when you add up the terms of a sequence instead of just listing them.

A series is the sum of the terms of a sequence, in contrast to the sequence itself, which is merely a list. The sum of the first $n$ terms, $S_n=\sum_{k=1}^{n}a_k$ , is the $n$ th partial sum; an infinite series sums every term of an infinite sequence, and — remarkably, for a geometric series with $|r|<1$ — infinitely many terms can still add to a single finite number.