1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Science Advisor
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Arc tan sum math help
  1. Limit of arc tan. (Replies: 6)

  2. Arc Length Help! (Replies: 1)

Loading...