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Math Help - sequence

  1. #1
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    sequence

    Hello,

    I have the following:

    A(x)=(x+1) + \frac{1}{2x^{2}-3x+1}

    How do I find a sequence a_{0},a_{1},a_{2},... such that A(x)=\sum_{i=0}^{\infty} a_{i}x^{i}

    Thanks.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: sequence

    Quote Originally Posted by surjective View Post
    Hello,

    I have the following:

    A(x)=(x+1) + \frac{1}{2x^{2}-3x+1}

    How do I find a sequence a_{0},a_{1},a_{2},... such that A(x)=\sum_{i=0}^{\infty} a_{i}x^{i}

    Thanks.
    \frac{1}{2x^{2}-3x+1}=\frac{1}{(1-x)(1-2x)}=(1-x)^{-1}(1-2x)^{-1}

    You could now expand using the binomial theorem.
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  3. #3
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    Re: sequence

    Could you elaborate a bit. It's not quite clear. I mean, when expanded how do I include x+1 ?? Assistance would be appreciated!!!
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Re: sequence

    Quote Originally Posted by surjective View Post
    Could you elaborate a bit. It's not quite clear. I mean, when expanded how do I include x+1 ?? Assistance would be appreciated!!!
    (1-x)^{-1}(1-2x)^{-1}=(1+x+x^2+...)(1+2x+4x^2+...)

    After simplifying the above expression, simply add x+1 to obtain the required power series.
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