1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Convergence or divergence

  1. Apr 26, 2015 #1
    1. The problem statement, all variables and given/known data

    ∑ tan(1/k)

    show that it is convergent or divergent

    2. Relevant equations

    3. The attempt at a solution
    i used ratio test, but it's equal to 1, it means no works...
    i used divergence test, it equals to 0, no work too...
    so what should i do? i dont know how to use comparision test to attempt this problem
  2. jcsd
  3. Apr 26, 2015 #2


    User Avatar
    2017 Award

    Staff: Mentor

    What is tan(0.001)? tan(0.0000001)? Do you see some function that looks similar and could be used for comparison?
  4. Apr 26, 2015 #3


    User Avatar
    Homework Helper

    Use the result that if [itex]0 < x \leq \frac12\pi[/itex] then [itex]\sin x \geq \frac{2x}{\pi}[/itex] to show that [tex]
    \tan\left(\frac1k\right) \geq \frac{2}{\pi k}.[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted