## Mathematical Analysis## Sequences and Series |

## What does it mean if a series is convergent? |

Convergence of a series is related to the convergence of a sequence, but don’t confuse them. The convergence of the sequence of partial sums (usually written as *{s _{n}})* differs greatly from the convergence of a sequence of numbers (usually written as

*{x*For example, the series Σ

_{n}}).*x*(and its associated sequence of partial sums, or {

_{n}*s*

_{n}}), is convergent if and only if the sequence

*{s*is convergent. Thus, the total sum of the series is the limit of the sequence

_{n}}*{s*, seen as:

_{n}}