### 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.

### Alternating Series Test

For an alternating series

, if the series

is decreasing and passes the divergent test, the alternating series converges.

### Ratio Test

For the series

, if the limit

is less than 1, the series converges. If L > 1, the series diverges and for L = 1, the test is inconclusive.