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Convergence of arctan(2n)

  1. Nov 13, 2007 #1
    For the sequence {arctan2n}, it is bounded by pi/2, so does that mean it converges to pi/2, because the limit of f(x) = L, and therefore the limit of the sequence is pi/2?
     
    Last edited: Nov 13, 2007
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  3. Nov 13, 2007 #2

    EnumaElish

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    Here is an example of a sequence: 1, 1/2, 1/4, 1/8, ...

    It is bounded by 1, but does not converge to 1.

    Therefore, you need other conditions.
     
  4. Nov 14, 2007 #3
    Your other condition is that its monotonic increasing in n. And there's a theorem that says it converges to the sup of {arctan(2n): n>0}, which is pi/2.
     
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