đặt \(A=\frac{1}{10}+\frac{1}{15}++\frac{1}{21}+...+\frac{1}{120}\)
\(A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(A=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(A=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(A=2\times\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(A=2\times\frac{3}{16}=\frac{3}{8}\)
\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+.....+\frac{2}{240}=2X\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(C=2X\left(\frac{1}{4X5}+\frac{1}{5X6}+\frac{1}{6X7}+....+\frac{1}{15X16}\right)\)
\(C=2X\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+....+\frac{1}{15}-\frac{1}{16}\right)=2X\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)
