Question

\(\frac{8}{56}+\frac{8}{140}+\frac{8}{260}+...+\frac{8}{1100}\)=?

Answer 1

\(=\frac{4}{28}+\frac{4}{70}+\frac{4}{130}+....+\frac{4}{550}=\frac{4}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{22.25}\right)\)

\(=\frac{4}{3}.\left(\frac{7-4}{4.7}+\frac{10-7}{7.10}+\frac{13-10}{10.13}+...+\frac{25-22}{22.25}\right)\)

\(=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{22}-\frac{1}{25}\right)\)

\(=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{25}\right)=\frac{4}{3}.\frac{21}{100}=\frac{7}{25}\)