I am having a hard time proving this result. Could someone give me a hand? Thanks.
If $\displaystyle \sum {a_n}^2$ and $\displaystyle \sum {b_n}^2$ converge, then $\displaystyle \sum a_n b_n$ converges absolutely.
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 $\displaystyle \sum \mid a_n b_n \mid$. Clearly, the sequence of partial sums is increasing. That should be enough to show convergence right?