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Proving an Infinite Series

  1. Jun 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Given an infinite series that follows the form [(xlna)^(n-1)]/n!
    n takes on integers from 0 onwards
    x all real numbers
    a all positive real numbers


    2. Relevant equations
    Maclaurin series expansion


    3. The attempt at a solution
    In which for the e^x series expansion plug in xlna into the x from e^x to obtain a^x which is the answer to the infinite summation. However, are there any other proofs besides using Maclaurin? Thanks.
     
  2. jcsd
  3. Jun 6, 2010 #2

    D H

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    Note that

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

    In other words the nth term of this series is [itex](ax)^n/n![/itex]. You have a different series. The nth term of your series is [itex](ax)^{(n-1)}/n![/itex].
     
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