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Harmonic factorial series sum

  1. Mar 13, 2017 #1
    1. The problem statement, all variables and given/known data

    What is the value of ## \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + ... ## ?

    2. Relevant equations

    I have no idea since it's neither a geometric nor arithmatic series


    3. The attempt at a solution


    My Calculus purcell book tells me that it is e - 1 ≈ 1.718

    But there are no ideas in it.
    Please help
     
  2. jcsd
  3. Mar 13, 2017 #2

    haruspex

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    Do you know how to find the Taylor series of a function? If so, consider ex.
     
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