Let be nonzero complex numbers. Suppose exists, and .
1. Show that if one of the series and converges absolutely, then so does the other.
2. What if or ?
For #1, I assume converges absolutely and trying to prove converges absolutely. That is, there exists such that for .
I tried to use what I have to prove this, but not getting what I want. Can I get some help?
I don't know #2...