Question

1/2x4x6+1/4x6x8+1/6x8x10+......+1/50x52x54

Answer 1

\(\frac{1}{2.4.6}+\frac{1}{4.6.8}+\frac{1}{6.8.10}+..+\frac{1}{50.52.54}\)

\(=\frac{1}{4}.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+....+\frac{1}{50.52}-\frac{1}{52.54}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{2.4}-\frac{1}{52.54}\right)\)

\(=\frac{1}{4}.\frac{175}{1404}=\frac{175}{5616}\)