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Series Absolute Convergence Proof

  • #1

Homework Statement


If [tex]\sum[/tex]an2 and [tex]\sum[/tex]bn2 converge show that [tex]\sum[/tex]anbn is absolutely convergent


Homework Equations





The Attempt at a Solution


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

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Yes, you should. Better yet, use 2|ab|<a^2+b^2. Can you prove that?
 
  • #3
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
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
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.
 

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