_n$ in $\mathbb{C}$. Show that for every sequence $(x_n)_n$ in $\mathbb{C}$ for which the series $\sum_n x_n$ converges absolutely, that also the series $\sum_n \left(x_ny_n\right)$ converges absolutely.
* Suppose $(y_n)_n$ is a sequence in $\mathbb{C}$ with the following property: for each sequence $(x_n)_n$ in $\mathbb{C}$ for which the series $\sum_n x_n$ converges absolutely, also the series $\sum_n \left(x_ny_n\right)$ converges absolutely. Can you then conclude that $(y_n)_n$ is a bounded sequence? Explain!