Вычислите: 2/5*7+2/7*9+2/9*11+2/11*13+2/13*15+2/15*17

Решите задачу:

$\frac{2}{5*7}+ \frac{2}{7*9}= \frac{2*9+2*5}{7*9*5}= \frac{18+10}{7*9*5}= \frac{28}{7*9*5}= \frac{4}{9*5}$

$\frac{4}{9*5}+ \frac{2}{9*11}= \frac{44+10}{9*5*11}= \frac{54}{9*11*5}= \frac{6}{11*5}$

$\frac{6}{11*5}+ \frac{2}{11*13}= \frac{6*13+2*5}{11*5*13}= \frac{88}{11*5*13} = \frac{8}{13*5}$

$\frac{8}{13*5}+ \frac{2}{13*15}= \frac{8*3+2}{13*5*3}= \frac{26}{13*15}= \frac{2}{15}$

$\frac{2}{15}+ \frac{2}{15*17}= \frac{2*17+2}{15*17} = \frac{36}{5*3*17}= \frac{12}{5*17}= \frac{12}{85}$