\(A=\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.400}\)
\(A=\frac{1}{299}\cdot\left(1-\frac{1}{300}+\frac{1}{2}-\frac{1}{301}+\frac{1}{3}-\frac{1}{302}+....+\frac{1}{101}-\frac{1}{400}\right)\)
\(A=\frac{1}{299}\cdot\left(1-\frac{1}{400}\right)\)
\(A=\frac{1}{299}\cdot\frac{399}{400}=\frac{399}{119600}\)