Question

\(\frac{5}{2x4x6}+\frac{5}{4x6x8}+\frac{5}{6x8x10}+...+\frac{5}{16x18x20}\)

Answer 1

\(A=\frac{5}{4}.\left(\frac{4}{2.4.6}+\frac{4}{4.6.8}+\frac{4}{6.8.10}+....+\frac{4}{16.18.20}\right)\)

     \(=\frac{5}{4}.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+\frac{1}{6.8}-\frac{1}{8.10}+....+\frac{1}{16.18}-\frac{1}{18.20}\right)\)

    \(=\frac{5}{4}.\left(\frac{1}{2.4}-\frac{1}{18.20}\right)=\frac{5}{4}.\frac{11}{90}=\frac{11}{72}\)