Đặt B = \(\frac{3}{1.8}+\frac{3}{8.15}+...+\frac{3}{106.113}\)
\(\frac{7}{3}B=\frac{7}{1.8}+\frac{7}{8.15}+...+\frac{7}{106.113}\)
\(\frac{7}{3}B=1-\frac{1}{8}+\frac{1}{8}-\frac{1}{15}+....+\frac{1}{106}-\frac{1}{113}\)
\(\frac{7}{3}B=1-\frac{1}{113}=\frac{112}{113}\)
\(B=\frac{48}{113}\)
Đặt \(C=\frac{25}{50.55}+\frac{25}{55.60}+...+\frac{25}{95.100}\)
\(\frac{1}{5}C=\frac{5}{50.55}+\frac{5}{55.60}+....+\frac{5}{95.100}\)
\(\frac{1}{5}C=\frac{1}{50}-\frac{1}{55}+\frac{1}{55}-\frac{1}{60}+....+\frac{1}{95}-\frac{1}{100}\)
\(\frac{1}{5}C=\frac{1}{50}-\frac{1}{100}=\frac{1}{100}\)
\(C=\frac{1}{20}\)
\(\Rightarrow A=\frac{48}{113}-\frac{1}{20}=\frac{847}{2260}\)
HT
