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Does the series arctan n converge?

  1. Mar 1, 2011 #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. Mar 1, 2011 #2

    micromass

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    What is [tex]\lim_{n\rightarrow +\infty}{arctan(n)}[/tex]?? Does this tell you something about convergence?
     
  4. Mar 1, 2011 #3
    pi/2, so by the test for divergence it must diverge! Ohh
     
  5. Mar 1, 2011 #4

    micromass

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    Correct!! A good advice: Always apply the test for divergence first!!
     
  6. Mar 1, 2011 #5
    Thanks :)
     
  7. Mar 1, 2011 #6

    Mark44

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    Especially since it's probably the easiest test.
     
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