\(C=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+........+\frac{3}{61.64}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.........+\frac{1}{61}-\frac{1}{64}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{64}\right)\)
\(=\frac{2}{3}.\frac{63}{64}\)
\(=\frac{21}{32}\)
\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{61.61}\)
\(=2.\frac{1}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{61.64}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{61}-\frac{1}{64}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{64}\right)\)
\(=\frac{2}{3}.\frac{63}{64}\)
\(=\frac{21}{32}\)
\(C=\frac{2}{1.4}+\frac{2}{4.7}+.....+\frac{2}{61.64}\)
\(\Rightarrow\frac{3}{2}C=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{61}-\frac{1}{64}\)
\(\Rightarrow C=\left(1-\frac{1}{64}\right):\frac{3}{2}=\frac{21}{32}\)
\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{61.64}\)
\(C.\frac{3}{2}=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{61.63}\)
\(C.\frac{3}{2}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{61}-\frac{1}{63}\)
\(C.\frac{3}{2}=1-\frac{1}{63}=\frac{62}{63}\)
\(C=\frac{62}{63}:\frac{3}{2}=\frac{124}{189}\)
\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{61.64}\)
\(C.\frac{3}{2}=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{61.63}\)
\(C.\frac{3}{2}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{61}-\frac{1}{63}\)
\(C.\frac{3}{2}=1-\frac{1}{63}=\frac{62}{63}\)
\(C=\frac{62}{63}:\frac{3}{2}=\frac{124}{189}\)
