A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

I have tried investigate the convergence/divergence of the following question, yet ended up with having it converging when it's supposed to converge: an = (-1)^n . (n+2)/(3n-1)

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    diverge*

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, it will diverge. Although the limit as n approaches infinity has that (n+2)/(3n-1) approaches 1/3, the (-1)^n multiplier will have your limit oscillate...it won't be able to converge.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so because (-1)^n diverges, by the theorem if one diverges all will diverge and therefore the sequence will diverge?

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Kind of...in order for a sequence to converge, it must head toward a single value - that's the motivation for the definition. As you have that (-1)^n thing attached, you won't have the case where you approach one value...you essentially approach two values: -1/3 and +1/3.

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I've got it! Thank you.

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No worries :)

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.