A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Math2400

  • one year ago

Does the series converge absolutely, converge conditionally, or diverge?

  • This Question is Closed
  1. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sum_{n=1}^{\infty} \frac{ (-1)^{n+1} }{ \sqrt{n} } \]

  2. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is an alternating series one. So bn=1/sq(n)

  3. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know it converges

  4. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1433702724096:dw|

  5. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    using p-series it's divergent......so the answer is 'conditionally convergent' ???

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

    conditionally convergent is correct

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

    Yes, conditionally convergent. You can show the absolute value of your a_n diverges by p-series. Then you refer to the altrnating series test and as you showed, its convergent under those conditions so yes, conditionally convergent.

  8. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks :)

  9. 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.