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Math Help - While I'm at it, here's an OGF that has a sticky wicket!

  1. #1
    Member oldguynewstudent's Avatar
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    While I'm at it, here's an OGF that has a sticky wicket!

    c_{0}=2,\, c_{1}=0,\,\, c_{n}=2c_{n-1}-2c_{n-2}\,\,\, n\geq2<br />
    \sum_{n\geq2}c_{n}x^{n}=\sum_{n\geq2}2c_{n-1}x^{n}-\sum_{n\geq2}2c_{n-2}x^{n}

    f(x)-2=2x(f(x)-2)-2x^{2}f(x)

    f(x)-2xf(x)+2x^{2}f(x)=-4x+2

    f(x)=\frac{-4x+2}{2x^{2}-2x+1}

    \frac{2\pm\sqrt{4-4(2)}}{4}=\frac{2\pm2i}{4}

    I'm just not sure where to go from here. Where ever that is, I've heard you can't get there from here. Any help would be greatly appreciated.
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  2. #2
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    Is the fact that the roots of 2x^2 - 2x + 1 are complex bothering you?

    If so, just march on and use partial fractions as if the roots were real. It should all work out in the end.
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