Exercises
[0FK](Proposed on 2022-12-13) If the series \(β_{n=0}^β a_ n\) and \(β_{n=0}^β b_ n\) converge absolutely, show that the series \(β_{n=0}^β c_ n\) converges absolutely and
\[ β_{n=0}^β c_ n =β_{n=0}^β a_ n β_{n=0}^β b_ n\quad . \]