Verify the additive and multiplicative inverse property for the rational numbers $\frac{-7}{17}$ and $\frac{17}{27}$.

$\frac{1}{1\times 2}+\frac{1}{2\times 3}=\frac{2}{3}$

 $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}=\frac{3}{4}$

$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}=\frac{4}{5}$

 Use your reasoning skills, to find the sum of first $7$ numbers in the pattern given above.