I'm totally stuck:
$a_n \in \mathbb{C} $ is defined for $n\in \mathbb{Z} $ and $\{ b_k\}_{k \in \mathbb{N}}$ is a sequence. The infinite sums
$ \sum_{n\in \mathbb{Z}} a_n := \lim_{N \to \infty} \sum_{n=-N}^{N} a_n$ and $\sum_{k\in \mathbb{N}} b_k$
are absolutely convergent. Show:
$(\sum_{n\in \mathbb{Z}} a_n) \cdot (\sum_{k\in \mathbb{N}} b_k) = \lim_{n \to \infty} \sum_{k=0}^{n} \sum_{2|l| \leq n-k} a_l b_k$
I'm pretty sure I have to use the Cauchy Produkt, but I can't figure out how.