Suppose the series ak (the k is subscript) converges absolutely and that the series bk is bounded.
Show that the series ak*bk converges absolutely.© BrainMass Inc. brainmass.com December 24, 2021, 4:46 pm ad1c9bdddf
Since bk is bounded, we know that there exists some bound M such that
|bk| < M for all k
( |bk| is "modulus of bk")
We also know that sum(|ak|)=N, (where N, of course, is ...
Multiplication of an absolutely convergent series and bounded series is shown to be convergent.