\(A=\frac{4}{2.5}+\frac{4}{5.8}+...+\frac{4}{98.101}\)
\(A=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{98.101}\right)\)
\(A=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{101}\right)\)
\(A=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(A=\frac{4}{3}.\frac{99}{102}=\frac{66}{101}\)
\(\text{Ta có: }\) \(A=\frac{4}{2.5}+\frac{4}{5.8}+...+\frac{4}{98.101}\)
\(=\frac{4.3}{2.5.3}+\frac{4.3}{5.8.3}+\frac{4.3}{8.11.3}+.....+\frac{4.3}{98.101.3}\)
\(=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+.....+\frac{3}{98.101}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(=\frac{4}{3}.\frac{99}{102}=\frac{66}{101}\)
