# Math Help - Convergence of series

1. ## Convergence of series

I am having a hard time proving this result. Could someone give me a hand? Thanks.
If $\sum {a_n}^2$ and $\sum {b_n}^2$ converge, then $\sum a_n b_n$ converges absolutely.

2. ## Re: Convergence of series

Hi jackie,

I think we can get what you're looking for using the Cauchy-Schwarz inequality. Give it a shot with this and let me know how it goes. Good luck!

3. ## Re: Convergence of series

Thank you for your help GJA. By using the Cauchy-Schwarz inequality I am able to get a bound for the sequence of partial sums of the series $\sum \mid a_n b_n \mid$. Clearly, the sequence of partial sums is increasing. That should be enough to show convergence right?