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Math Help - sum of the series

  1. #1
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    sum of the series

    Hey what is the sum of the series :

    1 + (1 + 2)/2! + (1 + 2 + 2^2)/3! +.....

    I know that the nth term is (2^n - 1)/n! .
    How does that help?

    Thanks
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  2. #2
    Member mfetch22's Avatar
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    Columbus, Ohio, USA
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    numerical estimation

    I'm thinking that this series is an expansion of a simpler function, but I'm not certain. Instead, since I couldnt see the pattern, I just numerically calculated it and heres roughly what I found to be the sum:

    4.6707742704716
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Recall that \sum_{j=0}^\infty \frac{x^j}{j!} = e^x...
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