of complex numbers is convergent
if the sequence
of partial sums
is convergent. The limit is called the sum of
. A non convergent series is called divergent
of complex numbers is absolutely convergent
if the series
If a series is absolutely convergent, it is convergent.
The converse is not true: for example, the alternating harmonic series is convergent,
but not absolutely convergent, thus it is conditionally convergent.
A convergent series which is convergent, but not absolutely convergent is conditionally convergent.