Question

\(\frac{4}{3.6}+\frac{4}{6.9}+.........\frac{4}{27.30}\)

Answer 1

\(\frac{4}{3.6}+\frac{4}{6.9}+...+\frac{4}{27.30}=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{27}-\frac{1}{30}\right)\)

                                                 \(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{30}\right)=\frac{1}{2}.\frac{3}{10}=\frac{3}{20}\)

Answer 2

      \(\frac{4}{3.6}+\frac{4}{6.9}+....+\frac{4}{27.30}\)

\(=\frac{4}{3}\left(\frac{3}{3.6}+\frac{3}{6.9}+...+\frac{3}{27.30}\right)\)

\(=\frac{4}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{27}-\frac{1}{30}\right)\)

\(=\frac{4}{3}\left(\frac{1}{3}-\frac{1}{30}\right)\)

\(=\frac{4}{3}.\frac{3}{10}\)

\(=\frac{2}{5}\)