Question

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

Answer 1

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

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

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

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

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