MathDB

27

Part of 2009 National Olympiad First Round

Problems(1)

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

Source: 0

4/28/2009
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=′latex−bold′>(A)</span> 1000<spanclass=′latex−bold′>(B)</span> 1005<spanclass=′latex−bold′>(C)</span> 1010<spanclass=′latex−bold′>(D)</span> 2009<spanclass=′latex−bold′>(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