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Infinite limit of inverse tangent series

  1. Jul 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Take the infinite limit of that sequence.
    ScreenShot036.jpg (click to expand)


    2. Relevant equations



    3. The attempt at a solution
    I have no idea where to start from, hints and ideas would be greatly appreciated.

    Thanks.
     
  2. jcsd
  3. Jul 6, 2011 #2

    tiny-tim

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    hi flyerpower! :smile:

    hint: (tanA - tanB)/(1 + tanAtanB) :wink:
     
  4. Jul 6, 2011 #3

    Ok, so tan(A-B)=(tanA-tanB)/(1+tanAtanB)

    and A-B=arctan[(tanA-tanB)/(1+tanAtanB)

    Now i think i should find some A and B so as :

    tanA-tanB=x
    and
    tanA*tanB=k(k+1)*x^2

    buuut i cannot still figure out what A and B should be
     
  5. Jul 6, 2011 #4

    SammyS

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    How about tan(A) =(k+1)x & tan(B) =kx ???
     
  6. Jul 7, 2011 #5
    LOL, it was so obvious, thank you:)

    It gives me pi/2 - arctg(x) which is arctg(1/x)

    Thank you both!
     
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