# Fractional differences

**Algebra**Level 3

\( \small \color{teal}{ (\frac{1}{2} + \frac{1}{3} + . . . + \frac{1}{2005}) \times ( 1 + \frac{1}{2} + . . . + \frac{1}{2004}) - (1 + \frac{1}{2} + . . . + \frac{1}{2005}) \times (\frac{1}{2} + \frac{1}{3} + . . . + \frac{1}{2004}) = \ ?} \)

State your answer as numerator denominator, for example for \( \frac{2}{5} \), you would write 25