- #1
Dustinsfl
- 2,281
- 5
Prove the Schwarz's and the triangle inequalities for infinite sequences:
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?
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?