A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

does this converge or diverge sigma n=1 to infinity 1/n^2 tan 1/n

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

    hmm, this is a tough one. going to have to bust out my calc resources =)

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

    check out this resource: http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

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

    you can use the squeeze theorem here , now we have the following:\[\sum_{n=1}^{\infty} \frac{\tan(\frac{1}{n})}{n^2}\] So by squeeze theorem we have : \[\frac{-\pi}{2} < \tan \frac{1}{n} < \frac{\pi}{2}\] divide by n^2 both sides and you'll get : \[\lim_{x \rightarrow \infty}\frac{-\pi}{2n^2} <\lim_{x \rightarrow \infty} \tan \frac{1}{n} <\lim_{x \rightarrow \infty} \frac{\pi}{2n^2}\] where : \[\lim_{x \rightarrow \infty} \frac{-\pi}{2n^2} = \lim_{x \rightarrow \infty} \frac{\pi}{2n^2} = \lim_{x \rightarrow \infty} \tan \frac{1}{n} = 0\] where series = a finite number = 0, then it converges, correct me if I'm wrong ^_^

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

    wow, great answer! medal'd

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

    lol, thank you ^_^

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

    but please check if there's any mistake :)

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

    can u please explain why tan of 1/n is b/w -pi/2 and pi/2

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

    first, graph tan (n) on paper, you'll notice that tan (whateve angle it has here) is between -pi/2 and pi/2 :)

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

    k

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

    if you sketch all tans on the graph, then you'll see different intervals that you can take ^_^

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

    other thatn -pi/2 and pi/2, depends on the tan that you want to choose, but I chose the simplest of all lol :)

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

    and how did u got from the inequality sign to the equal sign

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

    I didn't , I just applied the sqeeze theorem and wrote it down :)

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

    which says if limit of (a) as x -->infinity = 0 and limit of (b) as x--> infinity = 0 then limit of (c, the one that's in the middle) = 0 ^_^

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

    -pi/2 = a and pi/2 = b, so c = tan(1/n) ^_^

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

    k ty u for help

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

    u guys are brilliant in math ...........;)

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

    np ^_^ lol sath, I wasn't at all, but I worked hard to reach this level :)

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

    haha u all are deserving student .....best of luck..

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

    thank you, likewise :)

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

    am the student of medicine but only becauz of some iq question am here.....

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

    are you an expert at writng

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

    want to do a google doc \

  24. 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.