A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

is the following alternating series divergent or convergent series? (please show proof) ∞ ∑ (-1)^(n-1) cos(1/n) n=1

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

    Set your series = a(n). Then use a(n+1) like this: |a(n+1)/a(n)| Working this you will find eventually find: cos(1/n+1)/cos(1/n) which should evaluate to <1 and therefore be absolute convergent. I'm not used to evaluating series with trigonometric components though.

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

    doesnt that go to 1 and not < 1 since we take the limit to infinity using the ratio test

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

    You might be correct in that, I'm not a 100% sure, been a while since I did the infinite series. If it does evaluate to 1, you'd need to consider the different cases and evaluate from there.

  4. 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.