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Math Help - Maclaurin series

  1. #1
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    Maclaurin series

    Left this late, (as usual):
    Use known series to obtain the fourth degree Maclaurin series for:
     f(x) = ln(1-2x) + ln(1-x)

    quick help much appreciated!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Dr Zoidburg View Post
    Left this late, (as usual):
    Use known series to obtain the fourth degree Maclaurin series for:
     f(x) = ln(1-2x) + ln(1-x)

    quick help much appreciated!

    It is "known" that \ln(1-x)=-\sum_{n=0}^{\infty}\frac{x^{n+1}}{n+1}= g(x)

    Then we know that \ln(1-2x)=g(2x)=-\sum_{n=0}^{\infty}\frac{(2x)^{n+1}}{n+1}

    f(x)=g(2x)+g(x)=-\sum_{n=0}^{\infty}\frac{(2x)^{n+1}}{n+1}-\sum_{n=0}^{\infty}\frac{(x)^{n+1}}{n+1}=-\sum_{n=0}^{\infty}\frac{[2^n+1][x^{n+1}]}{n+1}

    Now just let n=0,1,2,3,4 to get your taylor polynomial of degree 4.

    Good luck.
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  3. #3
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    thanks a lot. Really appreciate it.
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