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Find the sum to infinite series

  1. Jan 10, 2013 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    cot^-1 3 + cot^-1 7 + cot^-1 13+.........


    2. Relevant equations

    3. The attempt at a solution

    I first tried to write the nth term of the series

    [itex]t_n = cot^{-1}\left( 2^n + (2n-1) \right)[/itex]

    Then I tried to calculate the limit as n→∞. But I simply can't do that. I mean I don't know how to calculate the limit.
     
  2. jcsd
  3. Jan 10, 2013 #2

    Ray Vickson

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    Your presentation is very confusing; use parentheses, like this:
    cot^(-1)(3) + cot^(-1)(7) + ... or use "arccot" instead of "cot^-1".
     
  4. Jan 10, 2013 #3

    utkarshakash

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    OK Here's it

    [itex]cot^{-1} 3 + cot^{-1} 7 + cot^{-1} 13+.........[/itex]
     
  5. Jan 11, 2013 #4

    haruspex

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    It's not at all obvious to me how 3, 7, 13.. is supposed to be generalised. Do you know that it is intended to be 2n+2n-1, or are you guessing?
     
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