A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
(Introductory Real Analysis) I'm trying to prove that the product of a bounded sequence and a sequence that converges to zero, itself converges to zero. I have the basic idea to start but don't understand some of the work my Professor did. Could someone help?
anonymous
 one year ago
(Introductory Real Analysis) I'm trying to prove that the product of a bounded sequence and a sequence that converges to zero, itself converges to zero. I have the basic idea to start but don't understand some of the work my Professor did. Could someone help?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\text{Given}\ x_n \rightarrow 0, \ y_n \leq M,\]\[\text{Prove that:} \ x_ny_n \longrightarrow 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\text{Given} \ x_n \rightarrow 0, \]\[(\forall \lambda > 0)(\exists \ J \in N)(\forall n>J), \ \ \ x_nc<\lambda\]\[(\exists \ M > 0)(\forall n \in N), \ \ \ y_n\leq M\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Applying the above to our problem: \[x_n  0<\lambda\]\[x_n<\lambda\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My confusion is here: \[(\exists \ J \ \epsilon \ N)(\forall n > J), \ \ \ x_n<\frac{\varepsilon}{M}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How does that last part come about? @Zarkon @phi

phi
 one year ago
Best ResponseYou've already chosen the best response.1you have \[ (\forall \lambda > 0)(\exists \ J \in N)(\forall n>J), \ \ \ x_nc<\lambda \] and that is true for all lambda's it looks like they decided to let lambda be epsilon/M .

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I had to move on, but I'd love to come back to this question sometime for my own sake, I frankly still don't get it.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.