Question

\(\frac{5}{1x3}+\frac{5}{3x5}+\frac{5}{5x7}\)

Answer 1

\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}=5\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}\right)\)

\(=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}\right)\)

\(=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}\right)\)

\(=\frac{5}{2}\left(1-\frac{1}{7}\right)=\frac{5}{2}\left(\frac{7}{7}-\frac{1}{7}\right)=\frac{5}{2}.\frac{6}{7}=\frac{15}{7}\)