Bài giải:

Có: $2\times \left( \frac{1}{1\times 3}+\frac{1}{3\times 5}+\frac{1}{5\times 7}+...+\frac{1}{13\times 15} \right)$

= $\left( \frac{2}{1\times 3}+\frac{2}{3\times 5}+\frac{2}{5\times 7}+...+\frac{2}{13\times 15} \right)$

= $\frac{3-1}{1\times 3}+\frac{5-3}{3\times 5}+\frac{7-5}{5\times 7}+...+\frac{15-13}{13\times 15}$

= $1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}$

= 1 - $\frac{1}{15}$

= $\frac{14}{15}$

      Đáp số: $\frac{14}{15}$