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Math Help - Taylor ans Maclaurin series

  1. #1
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    Taylor ans Maclaurin series

    given f(x) = ln (1+x)

    a) determine the taylor series for f(x) expanded about x=1

    b) what is the interval of convergence for the series in part A

    thanks a lot for your help
    K
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
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    Hi

    The Taylor series expanded about 1 is \sum_{n\geq 0}\frac{f^{(n)}(1)}{n!}(x-1)^n... but we don't know f^{(n)}(1). I suggest you try to guess what is f^{(n)}(x) using the first derivatives and then you'll show it using induction.

    f^0(x)=f(x)=\ln(1+x)

    f'(x)=\frac{1}{1+x}

    f^2(x)=-\frac{1}{(1+x)^2}

    f^3(x)=\frac{1}{(1+x)^3}

    f^4(x)=-\frac{1}{(1+x)^4}

    \ldots

    f^n(x)= \,?
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