Вычислите 1/2⋅5+1/5⋅8+1/8⋅11+1/11⋅14+1/14⋅17=

$\frac{1}{2\cdot5}=(\frac{1}{2} -\frac{1}{5})\cdot\frac{1}{3} \\\frac{1}{5\cdot8}=(\frac{1}{5} -\frac{1}{8})\cdot\frac{1}{3} \\\frac{1}{8\cdot11}=(\frac{1}{8} -\frac{1}{11})\cdot\frac{1}{3} \\\frac{1}{11\cdot14}=(\frac{1}{11} -\frac{1}{14})\cdot\frac{1}{3} \\\frac{1}{14\cdot17}=(\frac{1}{14} -\frac{1}{17})\cdot\frac{1}{3}$

Складываем

$\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+\frac{1}{14\cdot17}=(\frac{1}{2} -\frac{1}{17})\cdot\frac{1}{3} =\frac{15}{34} \cdot\frac{1}{3} =\frac{5}{34}$