MathDB

Function Summation Identity

Source: 2008 Philippine Mathematical Olympiad Problem 4

May 6, 2014

function

Problem Statement

Let

f:\mathbb{R}\rightarrow \mathbb{R}

be a function defined by

f(x)=\frac{2008^{2x}}{2008+2008^{2x}}

. Prove that

\begin{aligned} 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. \end{aligned}