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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 nth partial sum denoted by Sn.

Convergent Series

When the sequence of partial sums Sn 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 nth 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.
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