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Convergence or divergence

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

    ∑ tan(1/k)
    k=5

    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

    mfb

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    2016 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

    pasmith

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    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]
     
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