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Math Help - Convergence of a serie.

  1. #1
    Member javax's Avatar
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    Convergence of a serie.

    Hello. Need some help on solving this one:

    Review the convergence of the following serie:

    1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...+\frac  {1}{n!}+...

    Thanks in advance.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    that's a known series, try ratio test.
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  3. #3
    Member javax's Avatar
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    Ok, thanks.

    I knew it was convergent in the first place. By ratio test i see that it is convergent.
    I've tested for n=50 and I see that it converges to number e, it approximates up to 14 digits. But can I come to number e somehow analitycally?
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  4. #4
    Super Member Random Variable's Avatar
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    It's the Maclaurin series for  e^{x} evaluated at  x= 1
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  5. #5
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    \displaystyle e^x  = \sum\limits_{k = 0}^\infty  {\frac{{x^k }}<br />
{{k!}}}
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