Question 119
Let
$$
f(x) = \frac{2008^{2x}}{2008 + 2008^{2x}}, \quad x \in \mathbb{R}
$$
Prove that
$$
f\left(\frac{1}{2007}\right) + f\left(\frac{2}{2007}\right) + \cdots + f\left(\frac{2005}{2007}\right) + f\left(\frac{2006}{2007}\right) = 1003
$$
$$
f(x) = \frac{2008^{2x}}{2008 + 2008^{2x}}, \quad x \in \mathbb{R}
$$
Prove that
$$
f\left(\frac{1}{2007}\right) + f\left(\frac{2}{2007}\right) + \cdots + f\left(\frac{2005}{2007}\right) + f\left(\frac{2006}{2007}\right) = 1003
$$