\(A=\frac{7}{1.3}+\frac{7}{3.5}+.............+\frac{7}{99.101}\)
\(=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+........+\frac{2}{99.101}\right)\)
\(=\frac{7}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.......+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\frac{100}{101}\)
\(=\frac{350}{101}\)