Convergence of series

I am having a hard time proving this result. Could someone give me a hand? Thanks.
If and converge, then converges absolutely.

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!

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 . Clearly, the sequence of partial sums is increasing. That should be enough to show convergence right?