# Series

# Series Terms

## Get down with the lingo

### Series

Series is a sum of the terms of a sequence denoted by .### Alternating Series

An alternating series is one whose terms alternate between a positive and a negative sign.### Partial Sum

The sum of*n*terms of a series is called the

*n*th partial sum denoted by S

_{n}.

### Convergent Series

When the sequence of partial sums S_{n}converges the series is convergent.

### Convergent Sequence

If the limit of a sequence exists, the sequence is convergent.### Arithmetic Series

This occurs when the terms of a series form an arithmetic sequence.### Geometric Series

This occurs when the terms of a series form a geometric sequence.### Divergence Test

When the*n*th term of a series does not approach 0, the series is divergent.