$$\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} = \frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \frac{1}{7 \cdot 9} + \frac{1}{9 \cdot 11} = \frac{1}{2} (\frac{1}{1} - \frac{1}{3}) + \frac{1}{2} (\frac{1}{3} - \frac{1}{5}) + \frac{1}{2} (\frac{1}{5} - \frac{1}{7}) + \frac{1}{2} (\frac{1}{7} - \frac{1}{9}) + \frac{1}{2} (\frac{1}{9} - \frac{1}{11}) = \frac{1}{2} (1 - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} + \frac{1}{9} - \frac{1}{11}) = \frac{1}{2} (1 - \frac{1}{11}) = \frac{1}{2} (\frac{11}{11} - \frac{1}{11}) = \frac{1}{2} (\frac{10}{11}) = \frac{5}{11}$$
Ответ: $$\frac{5}{11}$$