Question

E= 7/4x7 + 7/7x10 =7/10x13+...+ 7/301x304

Answer 1

E= 7/4x7 + 7/7x10 =7/10x13+...+ 7/301x304

\(=\frac{7}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)\)

\(=\frac{7}{3}\left(\frac{1}{4}-\frac{1}{304}\right)\)

\(=\frac{7}{3}\cdot\frac{75}{304}\)

\(=\frac{175}{304}\)

Answer 2

E = \(\frac{7}{4.7}+\frac{7}{7.10}+\frac{7}{10.13}+...+\frac{7}{301.304}\) 

   =\(\frac{7}{3}.\frac{7-4}{4.7}+\frac{7}{3}.\frac{10-7}{7.10}+\frac{7}{3}.\frac{13-10}{10.13}+...+\frac{7}{3}.\frac{304-301}{301.304}\)

 = \(\frac{7}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{301}-\frac{1}{304}\right)\)=\(\frac{7}{3}.\left(\frac{1}{4}-\frac{1}{304}\right)=\frac{7}{3}.\frac{75}{304}=\frac{175}{304}\)