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 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
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.