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Math Help - Taylor series

  1. #16
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    d) Determine the Taylor series of f'(x) around x=0. Can you do so without using b)?

    isn't it the same thing as b), just without the first term i guess?? or no?
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  2. #17
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    Quote Originally Posted by @_@ View Post
    d) Determine the Taylor series of f'(x) around x=0. Can you do so without using b)?

    isn't it the same thing as b), just without the first term i guess?? or no?
    You have,
    f(x)=\ln (1-x)

    And that,
    f'(x)=-\frac{1}{1-x}
    But this is a geometric series that you should recognize,
    -1+x-x^2+x^3-... = \sum_{k=0}^{\infty} (-1)^{k+1}x^k
    Last edited by ThePerfectHacker; November 26th 2006 at 07:58 PM.
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  3. #18
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    how is it related to part b then?
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  4. #19
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    Quote Originally Posted by @_@ View Post
    how is it related to part b then?
    Ah if you differenciate,
    -x+\frac{x^2}{2}-\frac{x^3}{3}+\frac{x^4}{4}-...
    Term by term,
    -1+x-x^2+x^3-...

    (NOTE: I made a mistake in my other post about the geometric series. It is corrected now).
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