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Homework Help: Arc tan sum math help

  1. Jul 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the sum
    Arc(tan1/2)+Arc(Tan1/8)+...+Arc(Tan1/2*n^2)

    2. Relevant equations

    nothing

    3. The attempt at a solution
     
  2. jcsd
  3. Jul 3, 2008 #2
    Re: sum

    People still haven't gotten this part yet? :smile:

    Hadi, what have you attempted so far? As always, we don't do homework for you; you must show some effort before we do :wink:

    Is this an infinite sum?
     
  4. Jul 3, 2008 #3

    HallsofIvy

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    Re: sum

    And don't you mean Arctan(1/2), etc. rather than Arc(tan(1/2))- else you will need to define "Arc" for me!
     
  5. Jul 4, 2008 #4
    Re: sum

    How can I edit this one
     
  6. Jul 4, 2008 #5
    Re: sum

    You can't. Just post again this time with the correct sum.
     
  7. Jul 4, 2008 #6

    morphism

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    Homework Helper

    Re: sum

    Presumably the sum is
    [tex]\arctan\left(\frac{1}{2}\right) + \arctan\left(\frac{1}{8}\right) + \cdots + \arctan\left(\frac{1}{2n^2}\right).[/tex]

    If so, then what exactly does it mean to "find" this sum? If the goal is to simplify it, then this problem is similar to an old, well-known one that asks for a simplification of the sum
    [tex]\sum_{k=1}^{n} \arctan\left(\frac{1}{1+k+k^2}\right).[/tex]

    One of the ways of doing this is to first note that [itex]\arctan(k+1) - \arctan(k) = \arctan(1/(1+k+k^2))[/itex]*, and then telescope.

    If you can figure out how to get this identity, then you can play around to come up with a similar one that will solve your problem.

    It's also interesting to try to evaluate
    [tex]\sum_{k=1}^{\infty} \arctan\left(\frac{1}{2k^2}\right).[/tex]

    (* What's up with [itex]?)
     
  8. Jul 5, 2008 #7
    Re: sum

    thanks a lot my question is solved
     
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