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Math Help - Deriving Taylors for 1/(1-X)

  1. #1
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    Deriving Taylors for 1/(1-X)

    I am currently deriving Taylors for all n. I had to do one for 1/(1-x) and I came up with 1-x+x^2-x^3+x^4 instead of 1+x^2+x^3+x^4+...+x^n. When I take the derivatives of (1-x)^-1 I get F'= -(1-x)^-2 F''= 2(1-x)^3 F'''=-6(1-x)^4. Where am I going wrong?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by manyarrows View Post
    I am currently deriving Taylors for all n. I had to do one for 1/(1-x) and I came up with 1-x+x^2-x^3+x^4 instead of 1+x^2+x^3+x^4+...+x^n. When I take the derivatives of (1-x)^-1 I get F'= -(1-x)^-2 F''= 2(1-x)^3 F'''=-6(1-x)^4. Where am I going wrong?
    \frac{d}{dx}\frac{1}{1-x}= \left(\frac{d}{dx}(1-x)\right) \frac{-1}{(1-x)^2}=\frac{1}{(1-x)^2}

    CB
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  3. #3
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    Duh

    Im so used to seeing the (x-1) in the denominator I just take it for granted the derivative is 1. I definitly need to pay more attention to detail. Thanks.
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