Series Absolute Convergence Proof

harrietstowe · Jan 22, 2011

Homework Statement

If [tex]\sum[/tex]a_n² and [tex]\sum[/tex]b_n² converge show that [tex]\sum[/tex]a_nb_n is absolutely convergent

I think I should do something with the statement 2ab[tex]\leq[/tex] a^2 + b^2

Dick · Jan 22, 2011

Yes, you should. Better yet, use 2|ab|<a^2+b^2. Can you prove that?

harrietstowe · Jan 26, 2011

Hey sorry to return to this late but I am still pretty stuck on this. Dick, I don't think I know how to prove that

Dick · Jan 26, 2011

harrietstowe said:

Hey sorry to return to this late but I am still pretty stuck on this. Dick, I don't think I know how to prove that

Better late than never. Try using (|a|-|b|)^2>=0.