A=$\frac{1}{17}$ + $\frac{7}{17.27}$ + $\frac{7}{27.37}$ + ... + $\frac{7}{1997.2007}$
= $\frac{1}{17}$ + $\frac{7}{10}$ ($\frac{1}{17}$ - $\frac{1}{27}$ + $\frac{1}{27}$ - $\frac{1}{37}$ +...+$\frac{1}{1997}$ - $\frac{1}{2007}$)
= $\frac{1}{17}$ + $\frac{7}{10}$($\frac{1}{17}$ - $\frac{1}{2007}$)
= $\frac{1}{17}$ + $\frac{7}{10}$.$\frac{1}{17}$ - $\frac{7}{10}$.$\frac{1}{2007}$
= $\frac{1}{17}$(1+$\frac{7}{10}$) - $\frac{7}{10}$.$\frac{1}{2007}$
= $\frac{1}{10}$-$\frac{7}{10}$.$\frac{1}{2007}$
= $\frac{1}{10}$(7.$\frac{1}{2007}$)
= $\frac{1}{10}$.$\frac{7}{2007}$
= $\frac{7}{20070}$