Does the series arctan n converge?

  1. I'm sure it doesn't, but how do I find out?

    [tex]\sum^{infinity}_{n=1} arctan (n)[/tex]

    I thought about using the integral test, but it's not decreasing. Any hints?

    Could I somehow use proof by induction to show that its an increasing function?
     
  2. jcsd
  3. micromass

    micromass 18,668
    Staff Emeritus
    Science Advisor
    Education Advisor

    What is [tex]\lim_{n\rightarrow +\infty}{arctan(n)}[/tex]?? Does this tell you something about convergence?
     
  4. pi/2, so by the test for divergence it must diverge! Ohh
     
  5. micromass

    micromass 18,668
    Staff Emeritus
    Science Advisor
    Education Advisor

    Correct!! A good advice: Always apply the test for divergence first!!
     
  6. Thanks :)
     
  7. Mark44

    Staff: Mentor

    Especially since it's probably the easiest test.
     
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