\(A=1-\left(\frac{3}{2.10}+\frac{3}{4.15}+\frac{3}{6.20}+....+\frac{3}{198.500}\right)\)
\(=1-\frac{3}{2.5}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(=1-\frac{3}{25}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=1-\frac{3}{25}\left(1-\frac{1}{100}\right)\)
\(=1-\frac{3.99}{25.100}=\frac{703}{1000}\)