![[Graphics:Images/ComplexSequenceSeriesMod_gr_267.gif]](../Images/ComplexSequenceSeriesMod_gr_267.gif){kind=small}
,
then ![[Graphics:Images/ComplexSequenceSeriesMod_gr_268.gif]](../Images/ComplexSequenceSeriesMod_gr_268.gif){kind=small}
converges. In
other words, absolute convergence implies convergence for complex
series as well as for real series.Corollary 4.1.
If ,
then converges. In
other words, absolute convergence implies convergence for complex
series as well as for real series.
Proof.
Proof of Corollary 4.1 is left as an exercise in the book.