Series Absolute Convergence Proof

[harrietstowe]

Homework Statement

If $$\sum$$a_n² and $$\sum$$b_n² converge show that $$\sum$$a_nb_n is absolutely convergent

Homework Equations

The Attempt at a Solution

I think I should do something with the statement 2ab$$\leq$$ a^2 + b^2

 

[Dick]

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

 

[harrietstowe]

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]

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.