- Thread starter
- #1

If

$$

\sum_{n = -\infty}^{\infty}|a_n|^2 < \infty\quad\text{and}\quad

\sum_{n = -\infty}^{\infty}|b_n|^2 < \infty

$$

then

$\sum\limits_{n = -\infty}^{\infty} a_nb_n$ converges absolutely.

To show this, wouldn't I need to know that the |a_n| is bounded not the sum of squares?