In the previous section we saw that most of the convergence tests were applicable for series with positive terms. When, this is not the case, series can behave differently. In example 25.1.4(V) we saw that the alternating harmonic series
                
is convergent, while the harmonic series
                
is not convergent. To analyze such occurrences in detail , we make the following definition.

Definition:

Let be a series of real members.

(i) We say is absolutely convergent if the series is convergent.
(ii) We say the series is absolutely divergent if is divergent.
(iii) We say the series is conditionally convergent if is convergent, but is not      convergent.
(iv) We say the series is an alternating series if either
          
or