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f(1/2009) + f(2/2009) + .. f(2009/2009)

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April 28, 2009

Problem Statement

f\left( x \right) \equal{} \frac {x^5}{5x^4 \minus{} 10x^3 \plus{} 10x^2 \minus{} 5x \plus{} 1}. \sum_{i \equal{} 1}^{2009} f\left( \frac {i}{2009} \right) \equal{} ?
<spanclass=latexbold>(A)</span> 1000<spanclass=latexbold>(B)</span> 1005<spanclass=latexbold>(C)</span> 1010<spanclass=latexbold>(D)</span> 2009<spanclass=latexbold>(E)</span> 2010<span class='latex-bold'>(A)</span>\ 1000 \qquad<span class='latex-bold'>(B)</span>\ 1005 \qquad<span class='latex-bold'>(C)</span>\ 1010 \qquad<span class='latex-bold'>(D)</span>\ 2009 \qquad<span class='latex-bold'>(E)</span>\ 2010