Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Requiem

  • one year ago

Determine convergence or divergence. (-1)^n/(n^3) I know that I want to use the alternating series test. I used (bsubn) as 1/n^3 and (bsubn+1) as 1/(n+1)^3. I know that (bsubn) as n ----> infinity equals 0, but is (bsubn+1) less than or equal to (bsubn)?

  • This Question is Closed
  1. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or do i need to use a comparison test?

  2. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know that those two conditions have to be met for it to be convergent...

  3. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it \[\sum_{n=1}^{\infty}\frac{(-1)^n}{n^3}\]

  4. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes thats it

  5. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it not only converges, but it converges absolutely

  6. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    all you need for the alternating series to converge is that the terms go to zero, which thsee certainly do

  7. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok..in my book it says that (bsubn+1) has to be less than or equal to (bsubn) but also that (bsubn) has to equal 0 when the limit is taken...

  8. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but \[\sum_{n=1}^{\infty}\frac{1}{n^3}\] also converges, so this series is not just convergent, it is absolutely convergent as well

  9. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and i wasnt sure if the former was true

  10. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah only need the terms go to zero

  11. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, thanks satellite

  12. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sum\frac{(-1)^n}{n}\] for example converges, although not absolutely

  13. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hell, even \[\sum\frac{(-1)^n}{\ln(n)}\] converges

  14. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its converges conditionally right?

  15. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the last two i wrote are only conditionally convergent, the one you posted is absolutely convergent, a stronger condition

  16. Requiem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thanks you for your help! much appreciated

  17. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yw

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.