# Series

### Terms

### 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.Advertisement

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