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Taylor Series

  1. Apr 6, 2006 #1
    Hi everyone, I am completely stuck on the below problem. Would anyone like to give me a hint?

    This is the problem:

    Let

    f(x) = \sum {a(i)*x^(i)}

    for i=0 up to infinity

    given that f(0)= 0 , find the first three terms in the Taylor expansion about
    x = 0 of the function [tex]1/f(x)[/tex] .

    Thanks a lot!:smile:

    PS: also, for the expansion of [tex]e^{e^(x)}[/tex] is it OK to simply expand the entire function in one go by differentiating the entire thing (which is what I did) or does one have to split it up somehow?
     
    Last edited: Apr 7, 2006
  2. jcsd
  3. Apr 6, 2006 #2

    arildno

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    Improve your notation first.
     
  4. Apr 7, 2006 #3
    I tried to do it with latex but I don't know how to do sums? And strangely if I put Latex brackets around the first expression it generates a different image,namely [tex]exp^{exp^{x}}[/tex], instead of the sum formula. This is all very odd!
     
    Last edited: Apr 7, 2006
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