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Maclaurin Series Help

  1. Dec 6, 2008 #1
    Find the first few terms of the Taylor Series around x=0...?
    of the function

    f(x)= {x/(e^x - 1) , x =/ 0}
    {1 , x=0}

    the function is piecewise.
    up to and including the term involving x^2

    It says to not compute derivatives of f but to use the formula for the Taylor series of e^x


    x/(e^x-1) = x (1/(e^x-1)
    so.
    would that be x (1/ [tex]\sum[/tex](xn/n!) - 1)
    or maybe x [tex]\sum[/tex] (1 / (xn/n!) - 1))

    I'm not really sure where to start
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 6, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    Remember you only need terms up to and including x^2. 1-e^x=x+x^2/2!+x^3/3!+... Divide numerator and denominator by x. Now you've got 1/(1+x/2!+x^2/3!+...). You know an expansion for 1/(1+a), right? Use it. Throw away terms that are higher power than you are looking for.
     
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