• Support PF! Buy your school textbooks, materials and every day products Here!

Convergent series doubt

  • Thread starter Ryuzaki
  • Start date
  • #1
46
0

Homework Statement



Show by example that if Ʃan and Ʃbn are two convergent series, then Ʃ (anbn) may be a divergent series.

Homework Equations



N/A

The Attempt at a Solution



I've been trying long and hard to find an example for this particular case, but I'm unable to find one. I've found examples where Ʃan and Ʃbn are divergent, but Ʃ(anbn) is convergent. Can anyone please give an example? Thanks.
 

Answers and Replies

  • #2
938
9
I think it's true that if Ʃan and Ʃbn are absolutely convergent, then also Ʃanbn converges. So maybe consider series which are convergent, but not absolutely convergent.
 

Related Threads for: Convergent series doubt

  • Last Post
Replies
15
Views
851
Replies
4
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
3
Views
730
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
651
  • Last Post
Replies
2
Views
719
  • Last Post
Replies
15
Views
2K
Top