Question

G= 1/1*3*5 +1/3*5*7+ 1/5*7*9+...+1/95*97*99

Answer 1

\(G=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+.....+\frac{1}{95.97.99}\)

\(=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+....+\frac{1}{95.97}-\frac{1}{97.99}\right)\)

\(=\frac{1}{4}\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)

\(=\frac{1}{4}.\frac{3200}{9603}=\frac{800}{9603}\)