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Math Help - Maclaurin series - check my work

  1. #1
    Senior Member mollymcf2009's Avatar
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    Maclaurin series - check my work

    Cn someone check my Maclaurin series for:

    ln(1+x)

    I got:

    \sum^{\infty}_{n=0}  (-1)^n \frac{(n-1)!}{(1+x)^n}
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  2. #2
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    Quote Originally Posted by mollymcf2009 View Post
    Cn someone check my Maclaurin series for:

    ln(1+x)

    I got:

    \sum^{\infty}_{n=0} (-1)^n \frac{(n-1)!}{(1+x)^n}
    f(x)=\ln(1+x)

    Then

    f'(x)=\frac{1}{1+x}=\frac{1}{1-(-x)}=\sum_{n=0}^{\infty}(-1)^nx^n

    Now integrating both sides we get

    f(x)=C+\sum_{n=0}^{\infty}(-1)^n\frac{x^{n+1}}{n+1}

    And since f(0)=\ln(1)=0=C we get

    f(x)=\sum_{n=0}^{\infty}(-1)^n\frac{x^{n+1}}{n+1}
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