\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+....+\frac{2}{196.199}\)
\(=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+.....+\frac{3}{196.199}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{.7}+.........+\frac{1}{196}-\frac{1}{199}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{199}\right)\)
\(=\frac{2}{3}.\frac{198}{199}\)
\(=\frac{132}{199}\)