Series Absolute Convergence Proof

  • #1
harrietstowe
46
0

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
26,263
619
Yes, you should. Better yet, use 2|ab|<a^2+b^2. Can you prove that?
 
  • #3
harrietstowe
46
0
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
26,263
619
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.
 

Suggested for: Series Absolute Convergence Proof

  • Last Post
Replies
9
Views
8K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
534
  • Last Post
Replies
9
Views
5K
Replies
10
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
0
Views
1K
Top