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Homework Help: Sum of a ? Series

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data

    I have a question involving the sum of a series. I have already worked out a series, and the equation for a term in the series is:

    ((ln a)^n)/n!

    a is just a variable, and n is the position in the sequence

    a variation is:

    (ln a)*((ln a)^(n-1))/n!

    How would I start writing an equation for the sum of the series?




    3. The attempt at a solution
    I tried using the variation and treating it as a geometric series, with (ln a) as the first term, but that didn't work, for obvious reasons, since the second part isn't exactly the difference/scalar
     
  2. jcsd
  3. Feb 28, 2010 #2

    rock.freak667

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    For a minute let's make a quick substitution of x=lna

    does the infinite sum of xn/n! look familiar?
     
  4. Feb 28, 2010 #3
    Sorry, no. I haven't learned much more beyond simple geometric and arithmetic series
     
  5. Feb 28, 2010 #4

    rock.freak667

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    Have you learned the Taylor/Maclaurin series of ex?
     
  6. Feb 28, 2010 #5
    No I haven't
     
  7. Feb 28, 2010 #6

    rock.freak667

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    In that case, without using the direct result of


    [tex]e^x = \sum_{n=0} ^{\infty} \frac{x^n}{n!}[/tex]


    I am not sure how to get you a closed for solution.
     
  8. Feb 28, 2010 #7
    so eln a=a

    But is there any way to have an equation that would give you the sum of a given number of terms in the series?
     
  9. Feb 28, 2010 #8

    Dick

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    I don't think so. It's not a geometric series.
     
  10. Feb 28, 2010 #9
    Ok thanks a lot guys for your help
     
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