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Math Help - maclaurin series..

  1. #1
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    maclaurin series..

    Hi all,

    How can I show that the maclaurin series of f:R->R defined by f(x) = ln(1+e^x) begins
    ln2 +(x/2)+(x^2/8)-(x^4/182)

    thanks.
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  2. #2
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    Re: maclaurin series..

    Quote Originally Posted by Oiler View Post
    Hi all,

    How can I show that the maclaurin series of f:R->R defined by f(x) = ln(1+e^x) begins
    ln2 +(x/2)+(x^2/8)-(x^4/182)

    thanks.
    You Should know that the Maclaurin Series is given by

    f(x)=f(0)+\dfrac{f'(0)}{1!}x+\dfrac{f''(0)}{2!}x^2  +\dfrac{f'''(0)}{3!}x^3 +\dfrac{f^{(4)}(0)}{4!}x^4+...

    Just do the calclulations
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