Series is a sum of the terms of a sequence denoted by
An alternating series is one whose terms alternate between a positive and a negative sign.
The sum of n
terms of a series is called the n
th partial sum denoted by Sn
When the sequence of partial sums Sn
converges the series is convergent.
If the limit of a sequence exists, the sequence is convergent.
This occurs when the terms of a series form an arithmetic sequence.
This occurs when the terms of a series form a geometric sequence.
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.
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.