Convergence and divergence.
Definition 7.1.3
The series
of complex numbers is convergent if the sequence
of partial sums
is convergent. The limit is called the sum of the
series. A non convergent series is called
divergent.
Definition 7.1.5
A series
of complex numbers is absolutely convergent if
the series
is convergent.
Proposition 7.1.6
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.
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