5

Part of 2002 Taiwan National Olympiad

Problems(1)

Source: 11-th Taiwanese Mathematical Olympiad 2002

Suppose that the real numbers

a_{1},a_{2},...,a_{2002}

\frac{a_{1}}{2}+\frac{a_{2}}{3}+...+\frac{a_{2002}}{2003}=\frac{4}{3}

\frac{a_{1}}{3}+\frac{a_{2}}{4}+...+\frac{a_{2002}}{2004}=\frac{4}{5}

...

\frac{a_{1}}{2003}+\frac{a_{2}}{2004}+...+\frac{a_{2002}}{4004}=\frac{4}{4005}

Evaluate the sum

\frac{a_{1}}{3}+\frac{a_{2}}{5}+...+\frac{a_{2002}}{4005}

algebrapolynomialalgebra unsolved