TR-MO-R1 2009 Problem 27

$f(x) = \dfrac{x^5}{5x^4 - 10x^3 + 10x^2 - 5x + 1}$ ve, $1 \le i \le 2009$ için, $x_i = \dfrac{i}{2009}$ ise, $f(x_1) + f(x_2) + \cdots + f(x_{2009})$ toplamı kaçtır?

a) 1000 b) 1005 c) 1010 d) 2009 e) 2010

Official text Turkish Mathematical Olympiad, first round 2009 official paper, page 8. Quoted with source.

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