# Convergence of series

• Dec 8th 2012, 04:54 PM
jackie
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.
• Dec 8th 2012, 05:11 PM
GJA
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!
• Dec 9th 2012, 09:53 PM
jackie
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?