Simplify: $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \dots + \frac{1}{9 \times 10}$.

Each term $\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$. Telescoping sum: $(1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + \dots + (\frac{1}{9} - \frac{1}{10}) = 1 - \frac{1}{10} = \frac{9}{10}$.