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How to sum this series

  1. Nov 27, 2009 #1
    1. The problem statement, all variables and given/known data
    I just trying to sum this series, 1/(n!*n) n from 1 to infinity. also similar 1/(n!*n^2)


    2. Relevant equations

    [tex]\sum\frac{1}{(n!*n)}[/tex]
    [tex]\sum\frac{1}{(n!*n^2)}[/tex]

    3. The attempt at a solution
    I know[tex]\sum\frac{1}{n!}=e[/tex]
    [tex]\sum\frac{1}{n}=ln[/tex]

    My math technique is rusty, can any one help? thanks in advance. ciao
     
  2. jcsd
  3. Nov 27, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    The sum of 1/n isn't ln. It diverges. And both of those sums involve nasty non-elementary functions. I only know this because I looked them up. Why do you think you have to evaluate them exactly? A numerical approximation to both converges very rapidly.
     
  4. Nov 28, 2009 #3
    Thanks. I am doing study on statistics. On some topic I have sum up probabilities of infinite number of events. I have done numberical approximation with excel, and the result is equivalent to a specific event. I was trying to show why.
     
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